I agree with Nicole. Living together while she is involved with another man, or looking to date other men would be a no-go for me. I don't remember your exact housing sitch, but telling her that she can't live in the house with you while doing that would be an ideal boundary. If you would need to leave the house to live separately it is a more complicated issue because of the legal ramifications.
W 34 Me 42 Married 7 years together 8 0 kids 1 beloved dog BD 4/6/2018 I moved out 4/7/2018 I moved back in alone 8/05/2018 I file 3/06/2019 D official 5/7/2019