shes really controlling and she has no right to demand to see your house in the name of your children. Especially if it was not included in the decree. Good for you to stick to your boundaries!
If she pursues, talk to your attorney. My guess is that the most she could do is have a neutral social worker or CPS check it out... but I would imagine there would have to be an actual reason??? And if she makes up a reason she could lose child support no? False accusations are not looked highly upon. So save all your interactions.
A lot of walk away females still want control. I have an acquaintance that is one and she puts her ex husband through hell. She gets the title of primary custodian and receives child support, but he’s the one that is always watching her son while she works and dates. He takes every opportunity to be with his kid (and had to move away because our area is too expensive for him to afford). She’s very aware too. Told me how when he got a new girlfriend she started to cry and got upset. When he saw, that he offered to try to work things out with her. She told me as soon as he said that, she realized she didn’t love him or want him back. She also has been having bad luck with guys and she wants to keep ex husband on side in case things don’t work because he is good with the kids.