As a practicing family law attorney one issue which is constantly raised is whether it is okay for the child to be around a significant other. This can from the person with the new “friend” or the other side. In any case, my answer is that typically the Judge’s frown on allowing the child to know and/or be involved with boyfriends and girlfriends, at least that is the case in Dallas and Collin county. I would suspect it would be the same where you live.
I found an interesting article in the Florida Divorce Law Blog that discusses this very issue (or similar issue). They were citing an article from the Institute of American Values. I am not sure how reliable this information is, but it brings up the interesting topic of cohabitation. Read the article and report and form your own opinion on the subject.
Even if you do not believe the article or the source, I would have to tend to agree with the underlying theory that children would suffer from these potential short term relationships. This includes boyfriends and girlfriends in a divorce. Be smart about your choices of who you expose your children to.