There's a lot of speculation in here.. have a few facts.
1) if one of you wants something the other doesn't someone will need a court order
2) the starting point on that is mediation whether you need it or want it or not, you have to to try and come to an amicable solution without wasting the court's time
3) then you either agree and put that in front of a judge to become a financial order or you don't and you hand it over to the judge to decide what happens which also then becomes a financial order
All the rest is sort of noise.. very important noise but noise non the less.
I assume one of the owners would like to move on and not be attached to a house they no longer live in etc etc.. totally rational but not going to be resolved without a lot of legal work unless you can come to a conclusion amicably and even then it'll need ratifying so it's no longer open to dispute down the line.