Going through the same thing, long term mono -> Triad. I think it depends on the people involved. For some of the women we tried with it was harder and some were easier. Some women made my girlfriend more jealous, others not so much, and it's not just how "hot" they look. It mostly comes down to how receptive they are to her and compatible with her.
We haven't had any big issues so far and ours has been going on some months now. Now when I think about "problems" others have I think there must be some incompatibility there. That doesn't mean it can't be worked out.... but it just means something needs to be done. As to what needs to be done, in your case sounds like this woman isn't as receptive to you for some reason and it's putting a road block on the triad. Maybe he is feeding back into her wishes, who knows, as the outsider you probably have a distorted view of the actual going ons.
Maybe there is something you're doing that is setting off her jealousies? I would focus on her for a little bit, show her, at least for a little time, that you want to be with her more than the man. Maybe make it subtle, ignore some attention he is giving you and focus on her while he is doing it? Probably lots of little things you can do that I have noticed the new girl in our relationship does to me time to time. It's good sometimes for bonding to have "chick power" combined against a common enemy "the man".