Although your feelings are obviously valid, it's never a good idea to force your partner to cut someone out (unless it's about super bad issues, which this isn't).

Yes, he has tried, and probably will try. On the other hand, he has respected the boundary for many months too, because he probably figured out, your gf will not give in. It's not clear in your story why you got angry though. He's been respectful and he drove her home after a night out, without anything having happened other than some normal talks... Don't be the jealous gf.

In any case, trust your partner rather than distrusting the guy. I think your partner is more than fair to agree with only seeing him on family matters. Be grateful you have such a partner!

Conclusion: shake these feelings as you've reached another healthy agreement (first the boundaries, now the limited contact). If you say 1 more thing about it now, it seems like you're the toxic, jealous gf... Be mature, get past it.