What should I do with my home after divorce?

My ex-wife and I bought a house together in September 2005 when we were married. We had a baby in September 2006 at which point she stopped working until 2010. We got divorced and she moved out in September 2011. In essence, she contributed nearly 3 years out of nearly 10 years I have owned the house so when she moved out we agreed to have her name taken off the deed. She wants to buy a house now with her new husband but her name is still on my mortgage. I struggle to make payments but it is current still. My credit is shot due to divorce. She told me that she wants me to refi or sell the house. I would refi if I could, but I fear my credit wont even allow me to do that. But to sell the house? Is it right for her for me to sell the house I have been paying into for 10 years just to make it slightly easier for her to buy a house? Am I wrong to think she is asking too much? What can I do? By helping her, id be giving up a home ive been paying for alone most of the years and would have to start from scratch in order to make her chances slightly better at getting a new home. Her credit is also shot and I don't know how much her name being off the mortgage would help in light of her other credit issues. What should I do?

Read more: What should I do with my home after divorce?