Based on what I am reading here as I have nothing else to go on, she seems to have been accommodating and helpful since you split. She also bailed you out when you hit hard times, money from what I read you have not paid back and suggested come sale time she would seek repayment from the equity, which seems eminently fair. I am assuming she has no responsibility for the children you mentioned (they are not hers?) and now, after 10-12 years she is seeking to move on with her life, move away from a liability/investment that is offering her little and is looking for your support. Your current work situation, that of your wife and your children are of little concern to her and she has up to this point been very fair and gone above and beyond to help and support you.
You are now seeking to take advantage of that goodwill to ensure you are not removed from your house because it does not suit your situation and circumstances and it would seem have over leveraged your house (drawn down from the mortgage I am assuming, but will stand corrected) and so in the 10-12 years your house value has not increased. Looking at it purely black and white she is doing nothing wrong and you should perhaps work out how you might buy her share or accomodate he with a plan to sell at some point fixed in time.
Just noted your point on it being interest only. So for a period of time she has actually been paying for you to live in a house for zero benefit. She seems like a good person to me, I think she has every right to move on with her life now IMHO and you would be best placed to help her do that.
My 2p
Too further add if she is not paying the mortgage payments, which I may have got completely wrong here that changes it somewhat, but I still think she is within her rights to exit.