My girlfriend and I have joint ownership of a house. The mortgage is in my name. Upon break up what are my/our options?

The house we bought was my parents house. Being that her name is on the title I understand that she is part owner of the house. I have been paying the mortgage with no help financially from her. Which is fine since I make more money than her. We have both expressed that neither one of want move out. So I proposed that we sell the house. This was met with resistance. Can I make her sell her portion of the house? Can I make her remove her name on the title? What are our/my options? If we sell, Whatever the house sells at, is she entitled to half of the selling price? or what is left over, after the mortgage is paid off....How does this work? Thank you for time,