I'm going to tell my girlfriend to figure it out
Why are you letting your girlfriend figure something out for herself?
Because, she's a girl and girls can't solve problems while drunk.
You should be more precise and straightforward when you have relationship problems. Playing mind games just makes everything worse.
I'm not giving an inch in this relationship.
If you do not care about your relationship, then the other person may become unhappy and break up with you and you may regret doing that. If you love the person, then you should strive to make an effort in making both of you happy but if you really do not care about her, then I suggest you break up with her so that she could find someone that would be caring for her.