Busting, I would not allow your H to bring his buddies to the house anymore. The boundaries are not clear, i.e. Did he move out or not? If he's even introducing the OW to people, he should not be "hanging out" at your house or inviting anyone to stay in it. I would express this with kind politeness but firmly.
In regard to the cousin issue: Maybe you can say that given the situation, his cousin would be better off staying with him and the OW.
