I hope you will think about leaving your mom off the invite list for the party. That might solve the problem about her bringing other people and then she won't bug you about those other issues.
I would agree.
especially since you are focusing on the kids' friends, just make it a kids-only party and don't invite her.
If you want to, have her over for dinner some OTHER time. I do not include any grownups w/ my kids' parties. My MIL made a mention, and I just said, 'No, it for the kids' in a tone that was sort of "what planet are you from, again?"
For the other stuff, I'd just say, "Oh, are you still on about that? I don't understand why you can't just drop it."
CHANGE THE CONVERSATION. Make it suddenly be about how she can't drop the topic. Or about how you're surprised she wants you to commit fraud.