If she is a slob and already screwing around, if I was your brother I would get all the evidence of this and try to get custody of the child himself, sounds like the kid would be better off with your family than hers, then get a good lawyer and see if your brother could get the primary custody with visitations for the mother,sounds like he has a pretty good chance if he can get some proof of some stuff to take to court, and she can pay you child support. Its not like he would be doing injustice to his wife by taking the child, she would still get to spend time with the kid, but your brother would be responsible for all the major decisions made in the kids life, not to mention if the mother is this bad of a person, he wouldn't have to worry about such things as the kid seeing her bring men in and out of the house. I think the kids interest should come first and it sounds like it would be better off with your brother.
Good Luck