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1. As you say, I cannot give a definitive answer, but it seems foolish to force a sale (also bearing in mind these application are not quick applications to get through the courts) when you would be happy to sell once the work is completed. Are you able to put a realistic timescale on that? Perhaps this is where you should be focussing energy as ultimately it will be better for you both to have it sold and move on, if that's the decision. If it did go to court I think you have a good case for trying to maximise sale value by completing the work, but you do have to be realistic about timescales and the work can't drag on indefinitely.
2. If one is to remain permanently, then the remaining party would have to buy the other out.
3. If this is a temporary move, then it would normally be the party crying fo rah children that remains in the family home. Though if you are carrying out the work personally, you really ought to be there to do that...
If you cannot work it out amongst yourselves then yes mediation may be the way forward. Also apologies for the random typos in point 3. Not sure what happened there...
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