Live together with mom after 4th divorce

My mom recently got divorced for the 4th time. About 2 months ago now. Now, when I say recently got divorced I mean they signed the papers. The divorce is still not final. We bought a house together as my mom didn’t want to be alone. She told everyone she was going to take time to herself and not rush into a relationship like she always has. I don’t know why I thought things would be different than from my childhood. I now have my own family (husband and 4 kids).
My mother has never stayed single. Ever. She absolutely hates being alone and relies on everyone else around her to make her happy and validate her feelings. Love her because she is my mother but my siblings and I (5 of us) do not like her as a person. When she doesn’t get her way or looses control she uses guilt to get us to cave in to her desires. When all else fails she threatened suicide with all her husbands and children.
Literally right after signing the divorce papers she downloaded a dating app and started dating. She would talk about them. She mentioned a pilot that she was not attracted to and that he seemed super clingy and looking for marriage and that she wasn’t interested. She even said he was trying to use his job and how she would get free flights as a reason to date him. Well we brought up the house we both purchased together and wanted a discussion on what was fair. (One that should have happened before the house was purchased but she kept avoiding). Anyways she took off with this pilot guy right after only tk return for work then take off again for another week before she came back. Literally been 2 weeks and she asked if he could stay the night. A man we have never met with my 4 children in the same house. No I have a huge issue with her bring men to stay the men with me and my children.
When I was a child and she would date she always brought the men over. They never stayed the night however we frequently saw her in bed with some during the day. If she had a sleepover she did it at their place when my siblings were at our dads.
I am bewildered she would have 0 regard for bring men around my children. I wish she didn’t bring men around while I was a kid and I certainly will not let it happen with my children.
Again 2 weeks. A pilot she only ran to because she couldn’t handle a conversation. Today they both posted on Facebook that they are in a relationship.
If she lived by herself I could care less what she does with her love life. I do not want my family to be involved. I can’t simply move out because she can’t afford the home without us and I am worried she is going to cause issues selling the house.
Advice all around please.