Well, I think a happy little family bday sounds horrible!  I personally would not be involved - esp during a pandemic.  Its good BM is teacher the skids to honor their father on his bday....but does she really need to be there for the celebration??  It sounds like a bit much to me and would be a red flag.  Are they really divorced?  How long have they been divorced?  If they want to play happy little family maybe this isn't the right relationship for you.

My DH, early in our relationship, met at a restaurant with BM and SKs on SS's birthday "for SS." BM stole his car and house keys at the table (with plausible deniability of course).

He first told me about that little outing later that evening, and he nearly found himself with no GF as well as no keys. That's the last time BM successfully engineered a 'happy family' event.

Your BF should never be doing "just us family" events with BM, and personally I wouldn't do anything with his kids early in a relationship. 

Why exactly does BM have to be there? It's not a child's birth day. I see no reason for her to be there, boundaries are very important when dealing with skids and BM. Since it's early on it's best to set the tone right away. 

There is no reason for BM to be spending your boyfriend's birthday with him.  It is fine for the kids to celebrate wtih you and him, but not her.  From what you stated, she is also nutty... nothing good can come from it.  I would not step aside and allow him to play happy family without you either.  That is not what disengaging is to me.

I think it's perfectly fine for him to have a birthday dinner that includes his children.. and if you are to become serious about this guy.. you need to accept the fact that his kids are part of his life and will be part of it on many important occasions and holidays.  You don't need to take care of his kids.. but if he wants them at a birthday party etc.. I don't think that it's reasonable to tell him he can't.  But.. definitely, it is ok to plan adult celebrations and kid celebrations.. where one of those might not fall on the "day".. or weekend whatever...

What is not acceptable is that his EX is being included in this dinner.  She can drop the kids off.. he can go pick them up.. but no way am I sitting down with an ex for dinner.  (did it one time for OSD wedding.. that is an exception).  A man who is still including his EX in his birthday dinner is not as available as you think.

The problem i have with this is BM being there. I think you should sort of dispassionately gauge your BF's feelings about spending his birthday with BM and the skids. Is he totally fine with it? Do they routinely spend time "as a family" together? If so, tel him something along the lines of "You go ahead. I won't be there. I think you guys doing things together is a little cozy for my taste and I don't find it appropriate for exes to be hanging out together if they plan to start separate lives with other partners. Have fun!" And be unavailable for a while. Not mean or pouting, just be busier than usual. See if he self-corrects. Now, if he is like "ew, no! We never do things together and i don't want to!" Say "good, i think it's best you fully separate and each form your own relationship with the kids." Maybe you could be there and celebrate with them, or, let him have his celebration with  the kids privately then have your own.  

That's how i wish i had handled similar things early in my relationship. Instead i got visibly upset, nagged, whined, and was painted as the "jealous girlfriend." 

Why is BM going to his birthday? He can celebrate with the kids on his own time.  So my answer is NO, absolutely do not go. Also, start working with him on better boundaries with BM, and do it NOW, before you get too serious, because given what you've said about her, she's going to flip her lid when he stops allowing her to do things like come to his birthday parties.  Better to find out now how he's going to deal with that.

As for the kids, don't rush to meet them, if it's early.

Being disengaged doesn't mean you have to never be around the kids, so doing the bday thing with him and the kids is fine. The ex can stay home.

You don't say exactly how "new" the relationship is, but one thing you do want to do, is get a feel for the whole dynamic that he has with his kids, so you don't want to totally avoid them but, again, depends on how far into the relationship you are.

The BM, on the other hand, you never have to be around and if he still wants to have get togethers with her, well, that tells you about that dynamic.

First. Big Red Flag.  If  BF wants a relationship with you he must not play happy First Family 

If bm wants to be included in this happy little family treat, it's not for your bf nor for his kids. No, bm wants to be there to put you in your place. She wants to make sure you understand that she was there first and will remain so, that you understand that her kids come before you and her with them. Trust me, she will not miss a chance the whole time to belittle you as often as she can. Don't let this woman set you up to tear you down.

Talk him out of this lunacy. His kids can come and you will be there or his ex comes and you won't be back.

Honestly, I'd probably just end the relationship.

Hear me out. It sounds like you're newly in this relationship and have already discovered that your BF lacks boundaries with his ex AND you want to avoid the kids as much as possible. Not just disengage from them, but avoid them. And these kids are YOUNG. You're talking about trying to find a balance where you don't interact with the kids while they're minors for over a decade, and then I assume continue to avoid them and family time throughout their lives (if your plan is to be with your BF for that long). 

What is it that makes you want to disengage? I have nothing against disengagement, but there are "right" reasons to do it and "wrong" reasons to do it. If you're doing it because "not my monkeys, not my circus", fine. But if you're doing it because BM is crazy and your BF has no boundaries, or the kids are hellions that your BF and/or BM won't parent, or you think disengagement means you can avoid all the drama ever, then you're using it wrong this early in the relationship. If those are already problems, then you have to work with your BF to make your relationship and mutual comfort a priority versus trying to hide from it in hopes that you'll feel better about it. The chances are that you won't long-term.

I would use this time to focus less on disengaging and focus more on the dynamics at play in these relationships. Does your BF stand up to BM? How does he behave when she texts? How does he react when you bring up an issue with his ex or his kids? I'd say now is the perfect time to spend some time with him and his kids to see how he parents (not that you should step in) so you can see if his behavior is sustainable for you in the long run. His parenting, kids, and ex will bleed over into your life in some way more than likely, and you need to know whether you want to deal with the bleed over even if you remain disengaged.