Ex refusing to take responsibility

[mjw001]

Long post, but here goes, thanks in advance for reading or any advice.
In a nutshell, ex had an affair, didn’t want to stop so we divorced, and she is with her new partner.
Unfortunately we’re still living under the same roof (not the new partner - I’m not that much of a doormat) - she wants to stay in (and keep) the house (which I pay fully mortgage and utilities on), but refuses to speak with lenders to arrange transfer of mortgage. I’m reluctant to move out as I cannot afford to pay a mortgage and rent another place, nor could I get a second mortgage. I also feel like I cannot trust her to maintain the mortgage if I don’t, so dont want any arrears/defaults to affect my future.
We haven’t sold up as we wanted to minimise disruption four our DD (5yo).
Since the discovery of the affair/relationship, she has amassed almost 10k in credit card debt/OD (thankfully not on joint cards/accounts), so is unlikely to be able to get the mortgage transferred or be able to take out a new one with her fiancé (who also has a debt history, I’m led to believe).
I’d consider buying her out, but the house feels toxic. I’ve not slept properly in almost a year, and have no idea what to do next. Any attempts by me at rational discussion or conversation are met with childish insults and threats to ‘make my life a misery’ or ‘take me for everything’.

Think I just needed to sound off, but if anyone has any suggestions or advice, it would be gratefully received.

How did you divorce without a financial agreement about the house, or maintenance, or everything else for that matter? One of the first things a solicitor should do is look at your assets and negotiate? How did you get a divorce without that happening!? She can't 'take you for everything' if you are already divorced?

Similar situation to me however he moved out. Mortgage was in his name and I could t get a mortgage at the time so we made an agreement that I would pay the mortgage and buy him out privately. We had solisitiors involved etc for agreements. However after I paid him off He stopped paying child support and reported me to the tax office as I wasn't declaring all my self employed income. If I did I wouldn't have been able to pay the mortgage. Anyway I then had to stop paying the mortgage and the agreements solicitors drew up alwere about as much use as a chocolate teapot. What I'm saying is all this was toxic to the kids involved and you need to give your little one a fresh start. She must pick up on everything. I know mine did. The house was sold and I felt so much better moving on to a new house he had nothing to do with. I know it's hard but you should too. Plus if you meet another woman she won't want to be in that house and that could in turn affect another relationship. Good luck and put the house up for sale and be happy. Life is too short.

Divorce without financial orders are possible and easy to do - we initially had verbal agreements - she would apply to take on the mortgage with me as a charge so she wouldn’t have to be initially saddled with such a large financial commitment. Should’ve got all that in writing at the time really...