I'm not seeing what the dilemma is - could you tell us a bit more to help us understand, please?

I think you're in Mama Bear mode.  In trying to protect your son, you're going to drive away your MIL.  I know, I did it with my exH.  For our first daughter I did most of the care while he worked.  So when he got home he was tired, and she really didn't know him.  If she got upset he'd try to comfort her, but in the end it was easier just to pass her back to me.  As she got older, she grew more attached to me, and it became even harder for others to comfort her.  To the point where eventually even her father would give up after just a few hours and pass her back to me.  Not becuase he didn't love her, just because I was so busy doing it "right" that eventually it was hard for her to trust anyone else!

Your MIL has an existing bond with a child old enough to play with, communicate her needs and enjoy.  Your son is only 1!  One year olds are a LOT of work.  Her sending him back to you after only a few hours isn't a reflection of her love for him.  It's a reflection of her age, her ability to comfort him, her ability to juggle two children.  She's gravitating toward the child that's easier.  Many grandparents would.  And she's not buying him things all the time because he's one.  And he doesn't care what was in the Easter basket, or what outfit his sister got.  He isn't really even aware it's Easter!  She chipped in on an expensive gift (playpen), buys him books, and is actually volunteering to take him for you instead of saying, well I can take GD, but not GS.  Honestly, I'd cut her some slack!  She's not being intentionally cruel, she's just a grandmother with the energy levels that go with it!

I'd suggest taking her up on the offer with a caveat.  Yes she can come stay with you for the first week.  But you should do a few test runs of a whole day first.  If she's overwhelmed having them both all day Saturday then you'll know it's not likely to go well for a week.  Also, I'd explain that you would greatly appreciate having her stay with you for a week.  And that it's easier to take care of both kids for that long in the environment they already know.  Their toys are there, the crib, their beds and special items.  Food that they're familiar with etc.  That it would be easiest for all if she could come to you.  But if she can't, then you'll need to drop both kids off and pick BOTH kids up every day to her house.

And at the end of the day - consider your options?  Do you have the ability to take the time off?  With your babysitter gone, what are your options?

I wouldn't confront her.  I'd put yourself in her shoes, try to believe that she doesn't mean harm and do what you can to encourage the relationship with your son without comparing it to an older child's relationship.  You can mention it casually.  But unless you've mentioned it before many times and she's ignoring you, don't come out guns blazing!

As above comment - their ages are different, plus grandmas just naturally bond closer with grand daughters. They can shop and go to salon and naturally just like the same things.

Give gma some time and if it persists when your child is older, thats when you can confront. My SIL and brother dont allow my parents ANY time, and they so want to give my neice and nephew all kinds of presents. So I say let gma do and buy what she wants. But if your kiddo is 9 and shes not giving equally then I say approach her.

I'm going to also agree that with age.. her ability to deal with an infant vs an older child she has a bond with.. it's different.. and with what she has done.. and offers to do.. I would be really trying to give her the benefit of the doubt.  

If you feel something should be said.. your husband is the one to deliver a message to HIS mother.. NOT you.  He does it from his own POV.. NOT yours.. no  "well.. dw thinks you play favorites.. it upsets her you never buy anything for my son".. don't say that..   instead.. he says.  "Mom.. I'm sure you love both your grandkids.. but I notice that you do a lot for my daughter.. but not as much for my little boy.  He may not notice it now.. and it may just be his age.. but I want my kids to be treated as equitably and fairly as possible. "  she may come back with a "well.. I feel sorry for SD a child of divorce etc.."  and he needs to reiterate that SD is not abused and is just fine.. and he appreciates the interest his mom takes in her.. but hopes she will want to develop a bond with his other kids as well... and expects her to make that effort!"

as far as the babysitter situation... if it's just during the day.. perhaps it might work if you and your DH took part days of vacation during this time so grandma isn't as overwhelmed.. and it isn't such a huge prospect.. at least for the first week.. to see how things work out?  if she wasn't available.. you would both have to take time off work in any case.. so maybe take "some" time off but let her help pitch in.  IT doesn't sound like she hasn't been totally unwilling to be involved with your baby.. but he is a baby.. and babies can be more difficult.

I can relate. My MIL spends thousands (literally thousands) on SSs each year, but then buys DD (also, her grandchild) nothing or something she got on sale or at the thrift store. DD is a young toddler, so MIL will say, "she doesn't need anything" or "she doesn't know", but do SSs really need to be taken on vacation every year? Last year MIL took them on a two week vacation that cost her several thousand dollars - we know this, because she told us - and this week at Easter, she was talking to both SS about the trips she was planning to take them on this year - didn't talk to DH about any of this, either last year or the year before. She always acts like SSs are getting shortchanged. BIL does the same thing. He (and Silent SIL) gave SSs each a $100 bill for Christmas. For DD, they sent something cheap they got on Amazon that said "warning choking hazard - not for children under age 3" in big block letters on the front (DD was just over a year at the time). 

For DH's family, I think they are still bitter that he got divorced (he has been divorced for a decade at this point), think he never should have gotten remarried (I met him long after the divorce, so they can't blame me), and certainly think he should not have had more children (MIL told DH was "should have been more careful" when he told her that I was pregnant...as if DD was unplanned). MIL always tells him he is not doing enough for SSs, but really, she barely lets him do anything, since she is always stepping in and undermining him. 

My only saving grace is that MIL goes to Florida for almost four months in the winter. Now, she is back and she didn't see DD until Easter. She barely interacted with her and DD had no idea who she was. DH brought DD to SS's golf tournament yesterday. MIL was there (of course, she was, she took SS to play on the course the day before and then had him stay overnight so they wouldn't have to "drive too much"...all this without consulting with DH even though it was his weekend) and went to grab DD, who screamed, because she does not know MIL. Then MIL lamented the fact that DD screamed...but really, she doesn't try to build a relationship with her. She's been home from Florida for three weeks and has made plans with SSs several times, but has only seen DD on Easter and only yesterday because DH brought her. MIL came to the house on Saturday to pick up SS. She came to the door and talked to DH, did not inquire about DD, took some of our waters and left. 

All that said, this favortism from MIL drives me crazy, but I'll never say anything to her, because she'll just try to say I'm the problem. She's done that with me before when I told her I couldn't make holiday arrangements with Silent SIL (as MIL suggested after she (MIL) messed up the holiday plans), because Silent SIL doesn't speak to me. MIL just told me "oh, she's a bad communicator." Silent SIL has literally turned her back to me at events, has had one conversation with me in seven years, and multiple people at my wedding asked me what "her problem" was, but MIL wants to pretend that she's just a "bad communicator"? Ok, MIL. She will also say really mean things to DH about how he is just "at war" with BM and then claim that she doesn't or she will lie to DH about meddling with BM. So, it's not worth confronting her. When you are dealing with someone who is manipulative, they will always turn it on you, if you say something. This is especially true if other people in the family ignore the manipulation or dysfunction. It's always the person who speaks up who becomes the problem. In DH's family, they all know that MIL is manipulative, but they all want to pretend that she's just a loving grandma and mother. Their ability to look the other way is staggering, but they grew up in a family that prided itself on being a family other people admired, so it makes sense that they tried to hide the ugly parts of their family. 

Also, my advice, under no circumstances should you have your DS spend a week at grandmas. A 1 year old needs to see parents at night, also, this woman doesn't sound like someone you can trust to be a loving caregiver to a small child. 

You have two separate issues.

First is MIL. -There is no way she can keep both kids at her house for a week, if she can't keep the one year old there for a day. But, it is easier to watch children at the house they live in. All the items they need are there. But, I'd want a trial day soon to check whether this is feasible. MIL may not be able to physically keep with with an active one year old for several days.

if i were you, I'd look for a solution that does not involve MIL.

Second, you have a DH problem. He needs to speak to his mother. It is unacceptable to bring  an Easter bunny toy for one child (and none for the other) and give it in front of the younger child. 

What are your alternatives to MIL watching the kids during those two weeks?  If you have an alternative, use it for DS, even if you send SD to MIL.  If you don't have an alternative, I wouldn't say a word. 

Putting aside the babysitting, I also would not say anything to MIL about the favoritism.  I WOULD say something to DH and insist that HE address it with his mother, if not now then when DS is a bit older and it's clear that the disparate treatment will continue.  Frankly, I can see treating a 9 year old differently from a 1 year old.  I'm surprised that she doesn't want to spend more time with a sweet young grandson, but the gifts and the like wouldn't bother me - your DS doesn't know the difference yet.  If YOU bring it up, it could irrevocably damage your relationship with her and make family functions miserable for a long time.  Let your husband deal with his mother.

Is there any way you can work out each of you taking some time off. What if MIL came to babysit for 3 days, then you take off day 4 and husband takes off day 5, allowing grandma to go home and rest up? Maybe she even takes SD with her and returns Sunday night for 3 more days and you and hubby alternate on day 4 and day 5?

I'm sure you don't want to use up leave, but it seems like this is a bit much for MIL to do 2 weeks straight.