I have not read the whole thead....
1. If MIL is hosting the party, then she should be able to invite her son.
You can't control other peoples behaviors, only your own.
I would simply host the party elsewhere, and then you can choose the guest list in it's entirely.
2. If these people have actually quoted, verbatim, that they do not consider you and your daughter as family... Then, I would have to agree with you... simply set your boundaries and cut as many ties as possible. I would have no problem and have no guilt and no second thoughts.
3. I can very much understand your animosity towards these people. But, I am getting the hunch by skimming a few posts here that you have made this personal and are also issuing a lot of unnecessary personal judgements about them.
OP, you need to look a the big picture.
You need to take a good look at your own attitudes and actions.
No matter how awful these people are to you and your daughter, that does not excuse any tendency to be awful yourself. You are not responsible for other people's attitudes and actions. But, perhaps you can take a look at your own part in the stress and battles.
Learn how to take control of your own situation and responsibility for your own actions. If that means hosting your child's birthday party, and or cutting any close ties with this BIL, so be it.
But, as long as you stoop to their level and continue to 'engage', the situation will not improve.