But Moan - and others - what about the reason OP doesn't want them to go, which she's stated openly - FIL to be is a dick who is likely to dislike the fact that the children are there and use any disturbance to be nasty to OP/MIL and the family. Even if the children are well behaved, there's going to be what an anti-child grump will class as 'disturbance', everyone can imagine that.
OP's angry about MIL being an interfering twat. She's definitely reasonable there. But she says part of her decision making, before MIL tried to override her, was this issue with FIL, coupled with the fact that MIL and he could have put the wedding on the weekend and didn't.
It really doesn't seem to be all about being nasty to MIL, in advance of the phoning the school issue, why would it? OP describes the conversation as her saying, not sure about school, you could always move the time - offering MIL an alternative way the children could be at the ceremony. MIL is the one who waves off the objection with a 'you will comply with what I want' statement - as OP has said, things have to be her way or nothing...
OP should maybe have said straight out, I'm not having them at the ceremony because I don't want to get flack from your H2B if they dare to shuffle, I'd rather they come to the evening do and have a good time. Hopefully she's going to say that now, along with a reminder to MIL that she doesn't get to organise OP's parenting choices - and maybe see what MIL has to say to that. I imagine that if MIL was to apologise for phoning the school and see OP's point of view about FIL, maybe they could come to some arrangement.
Just because this issue has blown up, as things in families do, I can't see that as evidence that OP hates MIL with a passion. On the other hand, from my own experience with various dysfunctional oddities in my own family, I CAN understand OP very much not wanting to cave in to MIL after her trying to undermine her, and OP seeing that as important for their future relationship if MIL is a bit of a manipulator.