So you guys don't and never have sex? I am not saying you shouldn't be around them at all, but it is a tense, weird situation and him bring around his random...cuddle? buddies since you are saying you don't have sex may not help the situation. It is best for the relationship to solidify and become stable before bringing random others into the equation. It sounds like that never happened here.
What did you mean by he "keeps all her things from her"?