We are not married and have no children but the mortgage is in both of our names.
If she wont accept a reasonable offer, the court will set the price based on advice from 3 local agents and order her to pay costs of the court application.
At this stage she has no incentive to leave or sell as she is living free of charge!
You can tell her that you will ask the court to order mortgage payments you made deducted from her share. You are not responsible for mortgage or bills ofa house you don't live in, just to the lender.