You’re definitely going to attract lots of different views and opinions on this one OP.
Firstly, I don’t think the blame can all be on her. I know it’s difficult (I am a step parent) but it seems your partner hasn’t been the best either? I’d have cut him off at first sighting of the sexting. So I can see why you don’t like her - but he was the one in a committed relationship, not her. Albeit, I don’t agree with eithers behaviour.
If you really want to move on from everything he has done, then there needs to be a middle ground. IMO. Either you attend as a family unit together to co parent altogether. Or, you do separate things and he no longer goes with his ex wife but builds a life with his current children and you and his new baby.
I’ve always found it weird when people still go with their ex partners / husbands / wives on days out. It’s not for me. And DH also agrees. We’ve built a solid relationship together and when we have his son we do things as a family us three, without an ex.
We can all co parent amazingly together and DHs ex (maybe it’s because it was a one night stand so different) is really easy to get on with. But none of us would enjoy going out together for a day at the park.
Again- you’ll get some really mixed and divided comments on this. But I’d say my biggest concern is his sexting lol. That’s a big no from me.