Divorce stated house to be sold after 2 years, but then, ex died

[Chris Edgell]

So, my fiancee owned a house with her ex-husband. They divorced 10 years ago. Per the divorce, she would remain in the house and she and I would continue making payments for two years. After that time, she had the option of either buying him out, or the house would be sold and money split 50/50. So, after two years, the house was listed and we got ready to move. Unfortunately, he died suddenly before the house sold. At that point, things were far too crazy and we unlisted the house and didn't move, to make life easier and more stable for all.

Since then, not much has changed. We remain in the house, he remains on the title. She's dreading trying to move because she doesn't know what will happen with the title and his estate. There was never any sort of probate, and he had no will. Her plan has always been to sell the house (or refi) at some point, and when that happens, to split his half of the house and disburse it amongst the kids. (That's complicated too, as two are his biological kids - with her - but the oldest is the one she was pregnant with when they first met, and always treated him and thought of him as his own.) 

Her main question is how this will work. I know it won't be up to us, but I'm wondering what's most likely to happen. What she and I both think is fair is that the value to be split up should be the value at the time of his death, or what the house was listed for right before his death. So half of the value at the time of his death split amongst the kids, the remainder going to her. Especially because we have paid the last 10 years of mortgage payments. Obviously, the house value has gone up with the market and with improvements we've made (new roof, etc.). If the timing was different, I wouldn't have thought it fair if they took a huge hit to the value just because we waited to sell and the market fell in that time. It just seems like the value at time of death would be the natural choice, but I can't find any info on this sort of situation. Any thoughts? Thanks!