I have to be entirely honest, given ONLY this post, I think you're being a little unfair to your husband and his girlfriend. That's not to say that what you're feeling is wrong or inappropriate - you feel what you do right now and that needs to be validated - but you seem to think that your husband is being unreasonable without at least giving credit to the feelings, conflicts and choices he's going to have to make.
You mentioned that you have veto rules set up - that's cool, and perhaps your response here IS reasonable and clearly within the boundaries. I personally couldn't have a rule like that.
To me, the first and primary relationship is one with yourself. Any relationship that makes you comprimise YOUR principles or surrender your values is unhealthy.
Keeping in mind that I view the self-relationship as primary, you need to also realize that your relationship with your husband (and his toward his girlfriend) need to respect your husband's values. You have veto power over his partners - but you're not vetoing a partner here. You're vetoing his ability to invite his other lovers into his life and his home in ways that suit him.
Yes, it's your home and your life as well. Again, I don't mean to diminish that. But the way you phrased this comes across to me as an ultimatum. I'm convinced that in a relationship where people mutually agree and evolve a common set of values that ultimatums are entirely avoidable. When you find one it's because there is unspoken disagreement that should have been hashed out prior to the breaking point.
Your husband now has to evaluate what his girlfriend leaving means in their relationship. He also needs to evaluate what it means for YOUR relationship. Even if he agrees and asks her to leave, will he be happy in a household that gives eviction power to you rather than leaving those decisions up to consensus? You changed your mind about her living there after a long period of time. Can he feel stable in making decisions with you when one as large and as important to him ended up changing unilaterally?
I hope you guys are able to come to a mutually beneficial resolution and that your relationships get stronger for this. I also hope that you can empathize with his situation a bit and realize the decision may not be as clear cut as you seem to think it ought to be.
Connection is the path to passion. Passion is not the path to connection.