Ok thanks for the extra info.
The answer is that if you and she do not agree, the only way that she can be forced to sell the property is via a court order within divorce proceedings - ie only after a divorce petition has been filed at court, after which, either party can ask the court to decide how the matrimonial assets should be divided berween them if they cannot agree between themselves.
The family court has the power to make orders for eg the sale of a property, how the net sale proceeds should be divided between the parties etc. But the house will not be considered in isolation, but as just one of the matrimonial assets. These are everything in your name, everything in her name and everything you own jointly.
If your 15K of debt was for things that the house or you both benefited from, then you can argue that they are matrimonial liabilities and should be taken into account when deciding what each of your shares of the matrimonial assets should be. The same applies to any debts she may have.
The court starts from the position that everything should be divided 50:50 - then considers any reasons why that should not be so.
In your case, if the house is the only asset (ignoring her pension as I don't have that figure) and neither of you have any savings, and if your debts are matrimonial liabilities, then the net matrimonial assets are the equity in the house £257k - £75K = £182K, less your debts £15 = £167K. That is then divided by 2 = £83.5K each.
That means that you should get £83.5 plus £15K = £98.5K, so that you can clear your debts & end up with £83.5K. And she will get the remaining £83.5K.
If your wife wants to stay in house, she will have to buy you out - whether by remortgaging or via help from her family - the chances are that she won't be able to buy you out, in which case the house will have to be sold. Out of the net sale proceeds, you get £98.5K & she gets £83.5K.
If one person has a significnatly lower income than the other, then they can argue for more than 50% share, or if your marrriage was very short, and one person provided a signifcant lump sum as deposit, then they may also be able to argue for more than 50% share.
Going to court is stressful, time-consuming and expensive so to be avoided if at all possible. As long as you negotiate on the same basis that a court would decide the issue ie full financial disclosure to each other of all your finances, then you can negotiate either between the 2 of you, or via solicitors' correspondence, or via mediation. The family court anyway now requires the parties to have attempted mediationi before it will consider an application to court. Here's where to find a local mediation service:-
You would benefit from some face-to-face legal advice as well. Here's where to find a specialist family law solicitor:-
I hope this helps and I wish you the best of luck.
Thanks and best wishes...