Sorry Pippa but
(1) there is nothing to go to court about over ownership. Whether a 50/50 joint tenant or some other proportion TIC Kitty is entitled to her share. There can be no dispute, there is nothing to argue about she is a legal part owner, and has been for five years. It is indisputable. The ex cannot commence any legal action over ownership because there is nothing to contest.
(2) there is nothing that will get into court over the mortgage. Kitty had a contract to pay the lender, but there is no contract between Kitty and her ex, so she cannot owe the ex anything in connection with the mortgage. When the ex took total possession of the property and possibly moved in another, in lieu of the rent he owed Kitty for her half of the property he took over Kitty's liability to the lender plus the property upkeep. So all square. Nothing in connection with the mortgage or Kitty's rent will ever reach trial.
(3) It is quite possible for women to pay into the home and receive nothing out of the sale. But the circumstances would be totally different from the matter in hand. In the matter in hand Kitty will get her share, there will be no trial as there is nothing to contest, and Kitty's mortgage liability paid by the ex and the rent owed to Kitty by the ex cancel each other out.