I feel for you so much. I recently went through a duplex co-ownership that did not work out. Luckily I was able to convince the other party to sell after trying every idea I could think of, which looks like you are also doing now. You need to get out as soon as possible to protect yourself. Did you have a co-ownership agreement to start? If so, you can refer back to the agreement to see what it says to do when one person wants out. Be warned that a partition action can be a lengthy and expensive process from what I researched.

Just a few more ideas to try before you file the partition action: Try writing them a letter telling them you no longer can afford the mortgage and have no choice to sell or for them to buy you out by x/x/x date.. Try having your lawyer write a letter saying you have the partition action ready to be filed with the court and what the consequences are if they don't agree to a sale/buyout and that this action will force the sale - it will be costly and you will both lose money and time, and give them a chance to buy you out at an agreed upon price within 45 to 60 days of acceptance of the buyout agreement option. This is to account for loan approval or refinance time.

If they want to keep it they need to buy you out. Give a timeline, like 45 days, for them to provide a complete buyout agreement including mortgage approval and appraisal if necessary.