No!

How does dating a man make you responsible for caring for her when HE wants time away from her (and you!)?

That is REDICULOUS! 

You told him BEFORE he asked (demanded?), that you do not feel comfortable watching her and do not want that responsibility. 

NO. If you do not draw your boundary now, he will always expect this.

Haha! No, it's not part of dating someone with a kid, don't let ANYBODY tell you that. Your BF is the one who is being selfish.

If you give in to him, you will be setting a precedent and he will try to bully you into watching her more often, not to mention, bully you into other things that you don't want to do (like move in).

I am childless by choice, and have been with my DH for 23 years, since his daughter was 5. I have watched her a total of 4 hours (really 2 because she was a late sleeper) when DH had to work 1/2 a day on a Saturday and he asked me if I would. He has never once assumed that I should be in any way responsible for his kid.

And your BF now has added another teen to the mix? What an ass. Mental and anxiety issues or not, you have every right to say no to babysitting this man's kid. My SD was an easy kid, I still wouldn't have wanted to babysit her for an entire weekend, I am childess for a reason.

Please stick to your guns.

Parenting time is for the parent.  If he wants parenting time, he has to be there.  Or get CO amended.  If he is NCP, he is not obligated to take the kid, and he should tell the mom

Not that it makes a huge difference in my opinion - but why is he going to be gone all weekend?  Is it work related or social?

Tell him to hurry up and start looking for a sitter for that weekend because you are not going to babysit. 

You are in NO WAY responsible for this child. If he cannot be present for his visitation then he has to make other arrangements. You are not his nanny nor his maid. Do not let him get away with this!

You're not being selfish - he's being unreasonable. Why can't he just leave the kids with BM and not take his weekend if he's not going to be there to see them anyway? Since you've already told him you're not comfortable babysitting his kids and he expects it anyway, this does not bode well for the relationship.

Reading from your last post it comes across that your SO found himself a nanny to look after his daughter and is hopeful that once ha marries he can now rest easy knowing his daughter will have a caregiver long after he has passed.

Have you said NO? As in HELL NO? I would not have done this ever even as someone married to a man with a kid. And, best of all, he would never have expected or asked me to do this, not in a million years. Your not-SD can stay at her mother's for the weekend. 

But I get the feeling you are going to complain on here and then do it anyway. 

No.
Tell your BF No.
If he cannot understand English, tell SD NO: visitation is time with her father, not for you to babysit two teens.

Also make it clear to both these people who seem to share a genetic similarity of being hard of hearing that NO means NO.
You aren't there to facilitate his childcare duties when he is away.
Don't start or do favours like this because it blows up in your face.
SD can stay at Mom's house and play sleepover there.

You are being used and taken advantage of.
Put a stop to it by clearly saying NO.

If you can't get this message through, dump the user/loser.
Don't waste your time on someone who disregards you and uses you.

Look, you already had this discussion with him earlier in the week when she wanted to spend the night with you, and your BF agreed that you are not her babysitter. You were happy that he seemed to have your back. You had a discussion with him about never being alone with her for more than a couple of hours.

Do you see what he is doing?

This should not even be an issue, he knows how you feel about it, you have told him, "No."  Stop entertaining this nonsense.

How old is the other daughter?

He knows how you feel. But keeps trying to get you involved with his kids.  He needs another job where he home every night because his kids come first.  But it seems he comes first, his job comes second, kids third  you fourth, or is there something else .   

I don’t know how you can love someone who does not respect you. That is using you.  I know he wants that Happy Family thing.  Him, you, SK.  He did not get it in his first marriage. But you don’t want that. 

Your stepparent friend is a fool. Your bf is an asshat.

He is doing this in an attempt to FORCE you to skid-sit. 

Bottom line:
He expects you to play mommy. 
You don't want kids.

Move on. There are plenty of men out there with no children or adult children who are NOT looking for mommies. Woman, you are a CATCH. Drop this guy and move on.

Not only is he an inconsiderate presumptious asshole, a man with that much baggage isn't worth it. RUN

No. You are most definately NOT being selfish.

He is the selfish one in not stepping up and owning this.  He approved the sleepover. He can supervise.

Enjoy your weekend at the spa.

I want to give your friend the benefit of the doubt in maybe she means this could be something that might come with the committment of being married to this man, years down the line. But even then all stepparenting is dependent on how the individual feels. There's a spectrum of engagement that must be respected by the SO. 

Like most have said, definitely talk to him. And you need to be assertive! Take him by both shoulders, look him in the eye, and say: "Look. I am not doing this sleepover this weekend. I have already explained my reasons. Maybe I will be open to this someday, but this is not that day. It is unreasonable for you to expect this from me. My pace into this dynamic must be respected and you are not supportive. You trying to guilt me is not respecting my emotions and will do damage to the relationship." Stand your ground!! If he doesn't respect this and tries to threaten the relationship then I would take him up on the offer. You don't want that long-term.

No. No no no. No.

It's *his* weekend with his daughter. If he can't make it, she can have the sleepover at her mom's house. And he misses out on one of his weekends. You are not his proxy.

He does not reject you enough to discuss any of this with you before telling his daughter she could have the smell over when he won't even be there.   This guy is an ass.

Find a partner that is worth a shit.  Do yourself a favor.