Hello again and thanks for extra information.
To get her name off the mortgage will require the agreement of the building society. The court is not able to order the building society to remove her name, as the building society is not a party to the matrimonial case. The building society wants to minimise the risk to their loan, which is less if 2 people are named on the mortgage deed than if there is only one name. You don't say how much the mortgage balance is, but for the mortgage to be transferred into the husband's sole name, he would have to have an income equal to at least 1/3 of the mortgage outstanding, and the hiusband would also have to agree.
However, the court does have the power to a) to order that the house be transferred into your daughter's sole name (even if the mortgage stays in joint names), and to order that the house be sold - which if the husband continues to refuse to cooperate could be the answer. For example - the court orders the house to be transferred into your daughter's sole name, that then allows her to put the house up for sale, she can take him back to court if he refuses to cooperate with the sale, once an offer to buy has been received, if the husband refuses to sign the conveyancing papers, your daughter can get the court to sign in his place. The terms of the mortgage deed mean that the builkding society will get paid first out of the net sale proceeds. So then there is no more mortgage - and your daughter is no longer named on the deed, which is discharged.
It's not going to be a speedy process because the court will give the husband ample chance to show he can cooperate, and it's hard to get the court to move things along any more quickly.
Depending on all the other financial information which you didn't have, your daughter may or may not be able to keep some or all the net sale proceeds.
I strongly advise her to get some face-to-face legal advice from a specialist family law solicitor. Here's where to find one:
I hope this helps and I wish you the best of luck.
Thanks and best wishes...