I know some - well, a very few - custody agreements have written into them a principle of first refusal. Eg, if the kids are with parent A on a given day but parent A can't do it, then parent A is obliged to ask parent B first and only then arrange alternative cover (eg, parent A's new partner) if parent B cannot or will not do it. If you don't have such language in your residency agreement, though, then how your ex decides to arrange childcare is pretty much up to him.
How would you feel if, instead of him getting his new partner to look after the children on occasion, he paid someone whom you don't know to babysit? Would that be better, worse or similarly unacceptable as him asking his wife to do it? What I'm getting at is, is this an issue because your ex is not necessarily always there when the children are there, or is it more to do with whom he's choosing to cover for him?
Parent's evenings is a tricky one. Realistically, he can invite whomever he likes (as can you, of course). However, I would say this is one of those situations where a bit of give and take wouldn't go amiss. Eg, if he wants to bring his wife along then he could arrange to do so on a different occasion to when you see the teacher so you're not confronted with the both of them. I know my childrens' school is entirely open to helping out in such circumstances.
At the end of the day, a court isn't going to stop your ex's new wife from having involvement in your ("your" as in both your and your ex's) children's lives unless she's a registered sex offender or similar. If they're married then a court is going to view it as a stable relationship and, as such, it is inevitable that she will have contact and involvement with them.
The reason I asked about choice of educational path is because you're exactly right - that, and things like choice of medical care, are things that you and your ex are supposed to decide between yourselves. That's part and parcel of Parental Responsibility which your ex's new wife doesn't have. She is allowed to discuss these things with your ex, but the decisions are (supposed) to be made between you and him. But PR only affects major decisions about the children; day to day stuff is up to whomever the children are with at the time.
I know it's hard. I only found out that my ex had moved her new partner in with her when our kids came home and asked why mummy had a man staying at her house . But I also realised that there are some battles worth fighting, and some that aren't.