Ultimatums are one of those very heavy handed and powerful tools. They look like they can do the job in one fell swoop. The problem is that while they might drive the nail, the lack of finesse and control usually makes a huge mess of the entire project.
It's also been my experience that friendships also don't react well to force. Putting two kids with competing interests in the sandbox and telling them to be best buds usually ends up with one or both getting sand in the eye a short time later. Your gf at the very least seems very resistant to the idea... and given the sacrifices she probably thinks she made for the sake of your wife and marriage, she may be running low on goodwill to make such a venture seem like a good idea for her.
Frankly I don't think you have any easy answers to resolve this, and probably have some hard work, along with some tears and heartache ahead of you, no matter what. You need to figure out what you need and works best for you. Your gf needs to do the same for herself, and your wife likewise.
Maybe if you all figure those things out, then there can be a lengthy and detailed series of discussion about what that means for each of you, and if the various relationships are worth preserving, reviving, changing or dissolving.
I'd suggest trying to keep in mind that your gf is not part of your marriage, but she's still a person with her own needs, wants, and will. So like you and your wife, she deserves the consideration of making up her own mind about what's best for her. That may be a more standard relationship, and that may be struggling along with whatever type of relationship you're able to offer...if any. But she should get to make that determination, not have you try to make it for her.