First, regarding your title, it's not an either/or thing. Jealousy, compersion, lack of jealousy and lack of compersion are all normal.
We all have our triggers and it's good to know them. In your case, it seems your trigger is whatever he does with somebody else that you wouldn't or couldn't let him do with you.
It is possible that everything they do and you always do fails from making you jealous because you feel you are providing it too, but the second it's something that isn't in your relationship, there might be a fear he would leave you as a result.
I think it's normal to have this kind of feelings, but I want to assure you, there is no reason to blame yourself. You cannot personally fulfill 100% of someone's fetishes. The odds of finding someone whose fetishes match with yours completely are astronomical.
But you ARE providing him with fulfilling these fetishes. You are, because you guys are in a triad, and that's because you, personally, are not requiring monogamy.
What I mean is, there are several ways to be what you call "a good wife". If he wanted to learn to paint, maybe you wouldn't be able to teach him. But maybe you could help him find a class, and take care of the kids while he goes to it, or something to that effect. In that case, he'll get to learn to paint, and you'll have supported him and helped him.
And you can't beat yourself up because you don't know how to paint. You don't have to. He can go to other people for some things, being a good wife means being there for him, and finding solutions together.
Similarly, he can't fulfill all of your needs. It seems your GF is helping you a lot with the emotional stuff, both by making him more affectionate with you and by (did I read that right?) being affectionate with you as well.
That doesn't make him a bad husband. There was a problem in your relationship, you talked about it, you tried out something that is working for you. That's good.
Still, if you are still feeling bad about it, I suggest talking to him, or to both of them really. Explain that you feel like a poor spouse, and you just want to understand your feelings, talk it through, and hopefully at the end of the talk you'll be completely reassured.