Husband’s (ex)girlfriend’s Name Is Still On Our Home, We Are Trying To Refinance To Get It Off But Now She Wants Money.

(Location: Florida) Hello Reddit, my husband and I are currently in an unfavorable situation. My husband(49yr) male and I (33yr) female are currently in the process of trying to refinance to get his (ex)girlfriend’s name, as well as lower our mortgage payments. We have been together for 11 years, married for 9. My husband and his (ex) bought this home together in early 2014, they broke up shortly after and he moved out. After he moved out she was the only one making the payments, less then a year later she decided to move states for a job opportunity, she told my husband about it and he moved back into the home and took over the payments. His intention was to fix it up and sell it, however he and I started dating shortly afterwards, we got pregnant with our first born and decided to just stay in the home and make it our own. We tried to refinance back then but unfortunately he started having health problems which caused him to be in and out of the hospital, racking up medical debt in the process. His (ex) was aware of all of this. Well 10 years and 2 more kids later we are once again in the process of trying to refinance, she had previously stated that all she wanted was her name off, but now she’s claiming she wants us to buy her out. However I don’t agree with this, for many reasons of course. First she hasn’t paid for anything related to the home in almost 13 years, her and my husband took out a first home owners loan together($18,000) which we just found out we have to pay back. She also claims she replaced some appliances in the home when she lived here, but we have as well. Including having to replace the central ac unit twice. So Reddit my question is, if we decide not to refinance and just keep her name on. As the legal spouse of my husband, if anything were to happen to him would I have any claim to this home? And if he were to make a will regarding this home, would that help as well?