The danger is getting into a tit for tat over who paid for what etc. e.g. your fiance claims he paid most of the mortgage, his ex claims she paid most of the cost of raising their child etc. etc etc - things can start to get very messy.
As mentioned above, legally speaking she is one of the owners of the house (along with your fiance). And it is not unreasonable for her to want to sell a house that she owns, but no longer lives in - I think most people would do the same in her position.
There are two ways to sort this out:
1. You/your finance buy her out.
2. The house is sold, mortgage cleared, and both walk away - it appears that if the house was sold, once legals etc are paid, both would probably walk away breaking even.
I know some posters may not agree, but given the circumstances, the history and assuming the valuation is correct, if it were me, I'd go with option 2. It might be better for your fiance to get rid of the baggage associated with this house and both of you buy another house together.