Your situation sound similar to mine, though we don’t have a issue with the ex coming to the house. My husband put his foot down a long time ago with regards to the ex and the boundaries that are in place. She is not allowed at our home. He called the police department when she would show up at his house unannouced to “straighten things out” with me prior to their divorce. Other than last year at a mutual family friend’s funeral, I haven’t seen her in 3 years. I don’t go with him to “exchange” the children and I’ve never spoken to her. (I don’t respond well to yelling)
I’ve always sort of worried about giving the kids a key, but luckily, they have never needed one. This is the same reason I’ve never given them my cell phone number.
If there is absolutely no other alternative than that the child needs access to the home when you or the father is not there, is there a neighbor that you trust to hold a key? Putting a key on the property would be a better suggestion than giving it to the child to keep up with. Have the father let the child know that NO ONE is to be told where the key is for any reason. Maybe the ex will overlook the fact that the child has to be gaining access to the home somehow…
If the question does come up, she doesn’t have to be told anything except the child is able to gain access to the home. Then have the father put notice to his ex in writing that she is not allowed at your home without permission by him or you, not the kids. Make sure she knows that one of you must be there for her to be on the property. Though she may be unstable, she would still not get away with tresspassing, harrassment, or stalking. The law is on your side in this.
Install a security “camera” or let the neighbors know that she is not allowed. They have some that will show live feed without recording and they are minimal costs, or even a fake one that looks real just to give someone cause to wonder. Document everything.
The only issue I ever had was, what would I tell the children if I had their mother arrested for assault? But the one time that it nearly came to that, they witnessed it themselves and they saw me walk away. I never had the restraining order put on her because of them either. They love their mother and regardless of my “reasons” and their feelings towards me, it would still have affected our relationship negatively.