Your post said: just a big believer in if I play fair, she should be bound to those same rules
You are still asking other people to change your ex. The ONLY thing you can control is you. You cannot control your ex and neither can civil laws. You can document, but what we are all trying to say is that the ex will in all likelihood not be held accountable for these actions because they are small potatoes and not impacting the kids in a meaningful way.
In a perfect world, everyone plays by the rules. But they don't and you are wasting a TON of emotional energy on trying to change someone's behavior that doesn't want to change.
The court is not going to stop her from moving. They might tell her shame on you for moving without proper notice. They might not. She is moving in with that person. You have no control over it.