Is it accurate that the main problem is that they will be sharing the main space of the house, so while she will have her own room the rest of the house (minus his room) will be "hers" as well since it is shared space? That makes it awkward for you since you don't want to be going to HER place or THEIR place, but HIS place.
I think the only thing you could ask for is that they limit how many nights they sleep together. I mean, if she is paying rent, she has a right to have herself reflected there as well. (Once again, assuming that THAT is the part that is tough to swallow)
It seems like a tough situation since moving in together is usually a sign of the relationship becoming more serious, whereas for them it's really more of a convenience/financial step than an emotional one.
I do find it interesting that he is moving one of his girlfriends into his house when he is going through a divorce and custody battle. From what I've seen, ex-wives/mothers don't take too kindly to having another women brought in such close proximity to their kids too quickly. Why didn't he try to find a regular ol' roommate instead of moving in someone that he is dating?