You do not need the cooperation of your ex or the courts. You and/or your new partner need to sort out a new mortgage and use that to pay off the old one. If you can't get a new mortgage, you will have to leave things as they are or sell the property as it is unlikely that your mortgage provider will let you simply change the names on the mortgage.
Your issue is with the lender. Even if your ex wanted to be taken off the mortgage agreement, any changes must be agreed with the lender.