I'm so sorry. I don't know how you're managing, but you seem to be doing so great considering all you have to deal with. I've been following and reading, although I don't typically have the insight so many others can offer.
IMO, since she established residency elsewhere, you should have a reasonable expectation of privacy. She should have to get your permission to come in. Whether the law supports this, I can't say for sure.
But....it seems to me you now have grounds to file restraining order, or something legal so she can't come and go and take stuff.
I would check with your L , because I believe you can also get orders for her to return what she took from the home, if you can list the items. Even if not, try and picture the future....she's all alone in her home surrounded by the STUFF she had to have at all costs....but she'll be aaaallllllllll alone. Even if she wins the battle, you will win the war.
Her actions are not going to do her any favors in court. Keep the white hat on, Matt. At least YOU will still be able to sleep at night.
Your character is intact. It matters. I'm not talking just courts. I'm talking how it's impacting yourself and your kids. Trust me on this one.... I know from experience.