Legal Question in Family Law in Texas

The marriage issue is irrelevant, and almost certainly the answer is no, he can't be prevented from seeing them just because of this relationship. That said, I guess theoretically there could be reasons and scenarios where a court might order supervised visitation or at least a custody modification specifying that the kids couldn't visit if she was there--if she had abused them, if she was a convicted felon or had a history of violence or was a sex offender, if there had been some nasty, violent confrontation specifically between her and the kids' mom, if she kept telling the kids negative things about their mom and the dad showed no efforts to rein her in, etc.