"I will not promote a R between my kids and their father's gf."
Well, that's a relief :-p
Best thing is to stay out that R altogether, MYOB, not-about-you-ize it. Unless, of course, there is some present reason based on something that actually happens to think your children are at risk.
Don't manage their R with XH or with GF. Really not your job.
Now, when are you going to have a *great* playdate at your house? That will be fun to plan!
