I had a very similar case - the only sensible thing to do was to sell the house ( although of course I do not know if this is the case here). The ex wanted to buy out but at considerably less than market value. We didn't want to sell to her at that, issued Partition proceedings in the Circuit Court and it went all the way, 2 years, to the day - I do not think the ex believed that we would do this. The case was settled, the Court ordered the sale ( now by agreement) , there was a deal done on costs ( coming out of the sale proceeds) but it still cost a total of nearly 20K. Mind you, while we were fighting, house values did go up so there was a bit of swings and roundabouts. There is a huge cost in emotional damage done. But if two people cannot themselves settle the issues, if one party resolutely will not compromise or mediate, then I firmly believe in Court proceedings. The cases that end up costing are the ones that (a) should have been settled but (b) would never have settled without being landed on the steps of the Court. Harsh but true.
mf