@bnorthb,
Without the tie of a child, or shared property or a business or something like that, it doesn't make a lot of sense why she'd be in contact with someone who clearly hurt her, and more than one time.
I am thinking she could use some counseling. She doesn't have boundaries (as Ragman said; he's right) with this other guy and seems to have no problem letting him walk all over her.
You cannot make her get counseling, but there's no reason why you can't suggest it, and maybe even as a couple. E. g. you want to be able to deal with this, with a competent, unbiased professional.
And don't move in together. You're only adding financial issues on top of emotional ones, and that doesn't help anything.