So sorry.

Honestly I don’t believe you are required to allow unannounced visits. Since you separated she has not seen the kids. That means she needs to go through legal channels to establish official visitations. She can’t just show up. Honestly could you contact a lawyer and describe the situation. And don’t forget to add that she brought a boyfriend with her and offered to buy secret phones for her kid.

Typically parent who moved out can’t just show up, can’t just sit in your house, bring other people and give out cash. That’s not how it works.

Car likely belongs to a man. Not hers

And of course she looks young and pretty. She isn’t running household, working demanding jobs or two jobs to pay bills, paying mortgage and raising 3 kids. She lives alone in a small apartment, has ton of time to keep herself groomed and men take her out. Pretty easy life and it’s not hard to look fresh and young with this life style