He’s moving a crazy girl he just met into our daughter’s room. ADVICE!!

So I have been talking to my daughter’s dad recently about if he is moving out of his home or not. He has been really back and forth about it because he can’t afford it since I left him, but he also lives so close to us that he doesn’t want to move. I have been given him a lot of flexibility because I need to file our custody papers, but with his situation being so up in the air I have been waiting until he has set plans because I don’t want to file under the assumption that he will be living somewhere and then just have him move right after.

ANYWAYS. He called me and was talking to me about some girl he went on a date with (we are trying to be friendly so this was fine). Well this girl sounds batty. Like told him she was falling for him after one day, asking to meet our daughter (she met his 8 year old son on night 1), saying she will come see him regardless of where he lives, AND THEN she offered to be his roommate. I could not contain my laughter! He just kept saying how “this girl might actually be crazy and I might have to hide my car in the garage.” Well, then a few days later he calls me and tells me that he really does not want to move somewhere cheaper and that this girl will be moving in with him. He is using the extra room (that would have been the babies room which means our daughter won’t even have a bedroom) for her and she will live on the same floor as HIS SON. He knows NOTHING about this woman and seems like the only thing he does know is that she is weird.

I am not really ok with my daughter going to spend longer amounts of time over there until I know more about this girl or can at least run a background check based off of everything he has told me. He called me a bitch for even suggesting that. He said he needs a roommate and she is willing to pay half his bills plus sleep with him, so he can’t say no. I just think the situation is so unstable and freaking weird.

How should I handle this? Am I overreacting? I need advice here!