I would continue with the "neighborly niceties." If your W isn't comfortable with family dinners, then she can go elsewhere. Or she can sit there and stew in her uncomfortableness if she so chooses. No need to alter your usual family togetherness with the kids.
My H and I - when he was still involved with OW - attempted to do some things together with the kids, including cookouts, because S8 would ask. It often (okay, every time) ended up leading to H cake-eating. Sigh.
Maybe don't borrow trouble just yet by projecting alllllll the "what ifs." I think you have a VERY strong handle on where you are and what you feel is best for this sitch. Sometimes, planning for every "what if" accidentally gives you expectations. I don't think that's what's going on here. But I do know we could spend a day talking about what COULD happen. And the one thing we didn't think about will be the ONE thing that will come up.
Go with the flow this weekend. Trust yourself and all you've learned here in just the past few days. If she offers for you to go with her and the kids and you WANT to go for the kids, go. But I'd at least plan a time or two to get out of the house alone to GAL and handle your "exit strategy" just as Starsky has detailed.
Remember this is all soooo new, so it's hard telling how things will be. Focus on the few things you know you need to do FOR SURE. You have a great "gameplan" prepared.
You are confident, (neighborly) nice and quite the busy man all a sudden, who is a little mysterious and GAL now. Be cordial and friendly (but not too friendly).
I'd play the conversations by ear. I don't think it hurts to wear a smile and ask how a day was if it comes across as natural.
Remember: "I don't want any of this, but I won't stand in your way." That overriding thought may help guide you in making decisions on how to react/respond to things this weekend. Starsky may have a different opinion, but that's my .05 (as always, adjusted for inflation).
Will be thinking of you!
M: 40 H: 44 Married 14 years S11 & D6; D20 & D19 from previous M 2BDs/PAs, 8 years apart Piecing: April 2014