I doubt mil let’s you tell her what to do in her own house. Maybe dh could have a polite word with mil and say ‘our house our rules’. If it’s not going to cause too much trouble. Then see what happens after. 

Is MIL staying at your house for her visit? I think you should set a boundary with your DH that you won’t tolerate guests in your home who try to give you orders or who yell at you. If his mother continues to do that, then she’ll have to leave.

If your DH thinks that he can’t say anything because it’s his mother then he’s still a child, he’s not an adult. An adult can say something to another adult when that adult is acting rude regardless of his relationship with that other adult.

Your house your rules.  Your MIL has no right to come into your home & start dictating terms the way she is. If she doesn't like how things are done, she can stay elsewhere.  I do think that message should come from your DH, ideally, but if someone was yelling at me constantly for mundane, every day things I'd eventually lose my cool & tell her myself. 

Your DH is a Mama’s Boy, your MIL is staying there for the entire summer, and you are the one stuck disciplining your skid with no support from your DH. 

You are living the dream. I’d stop parenting in any way and let DH and his mother deal with it all. 

Actually, I’d divorce him, but that’s probably not what you want to hear. 

I have a MIL just like this. My DH stood up to her though.  Your first mistake is giving in to her demands. When she yelled at you about the laundry, I would have said, Excuse me but I didn't ask for your input. Then I would have repeated my request for SD.  If your DH won't set a boundary in your house, then it is perfectly acceptable for you to do it.  

Also, I would tell DH that his mom can no longer stay at your house if he refuses to set boundaries. This is 100% a DH problem.  Your DH doesn't want to deal with his mother, but she is disrespecting you and teaching SD to do the same.

Start asking MIl to help!.   Many wives have this issue when MIL comes to visit, they do not have the time to entertain guests.  DH needs to talk to her, and say can you watch baby for an hour or two every day so Mother101 can take a nap.  let SD have screen time.

What is your house rules.  That SD has jobs to do around the house like every one else.  

MIL goes, or you check into a hotel until she leaves. 

Lol, wow.

I can't imagine what would happen to a visitor in my house if they yelled at me.  No one has tried.

FIL is a big boss at the company he works for, he's used to getting his way.  One time when he was visiting, he yelled at one of the kids.  I stood face to face with him, arms folded shoulders back, and told him "We don't do that here."

He stammered and apologized, and hasn't been a problem since.  

Take back your power.  You are an adult.  A badass!  Unleash hell.

My MIL yelled at me.

I'm assuming you are not the confrontation type or one that doesn't like to address issues right away but your MIL yelling at you is disrespectful and you needed to shut it down right than and there. You are not a child and this is YOUR home, she has no authority there.

My husband isn’t doing shit. He says he can’t because it’s his mother.

Since your H lacks the b@lls to set boundaries and stand up for you, you will have to do it yourself or it will continue.

Wth do I do in this case?

You need to set strong and firm boundaries with your MIL. You have to have a talk with her and your H and make sure you are all on the same page. You can't properly raise SD because MIL is undermining your parenting. The kids see this and will only turn around and duplicate this behavior. You have a H problem and that has to be addressed 1st before having a coming to God meeting regarding the level of disrespect your MIL is displaying.

OP needs to master the frosty stare. 

When you ask SD to set the table... and MIL yells at you? 

Frosty stare.. accompanied by the words. "DH and I feel it's important to give kids responsibility.. You may set the rules in your own home.. this is our home.. our rules"

When she yells at you for taking away an item from SD.  "In this home, actions have consequences.. SD understands this"

You could also try the pre-emptive strike with your MIL and have a sit down during a quiet moment to discuss the situation with her.

"MIL, I know that you mean well and care about your granddaughter.  However, your son and I both believe that children that are given some responsibility and boundaries will thrive in the long run.  Chores teach her self reliance and give her a sense of accomplishment.  Things like cleaning up and putting her laundry in the hamper are setting lifelong good habits. Asking her to set the table gives her the ability to be involved in the meal and more part of the family effort to put a meal on the table.  When she watches her sibling for a short time, she is creating a bond and learning to care for others. When we take away a toy or electronic from her, we are not doing that to be mean.. but because she needs to learn that actions have consequences.  We would rather her learn these lessons in the safe environment of her HOME than from people that don't care about her in the cold outside world.  You may not agree with everything we do in this home, but everything we do is coming from a good place of caring for that little girl.  We hope you enjoy your visit, but in the future, please refrain from second guessing the rules and boundaries that we have established in our home"

Just tell her to STFU when she yells at you.