I think all that needs to be said has already been said, but I’ll add my two pennyworth just the same.
There is one thing I don’t understand here and that is just how you are currently funding the mortgage with little or no income. However I assume that you are somehow and in any case it is of no matter. The issue for your ex here is not so much the ownership of the house but the status of the mortgage on it. As has been said, she is responsible for (although she may not be funding) a mortgage on a house that she does not and practically cannot live in. Additionally this is affecting her in that she cannot obtain a further mortgage until she is released from that responsibility.
I’m by no means an expert in these matters but despite making some strange decisions from time to time, courts also have a history of making some common sense decisions too. There is every likelihood that if this matter went to court an order to sell would be made. It is clearly unreasonable for your ex to be tied to a mortgage on the property for the next twenty years or so. You mention that this is your home. Whilst it may be your home you do not actually own the property. Assuming you occupied the house as “tenants-in-common” you own it jointly with neither of you having a discreet share.
You need to resolve this situation because if you simply refuse to co-operate your ex may well go to court. It is unfortunate that you will, in all probability, have to move out. The alternative is for the two of you (as joint owners) sell the property to you as sole owner with some adjustment being made for the differing amounts of equity you each hold. However, from what you say, it is unlikely that you would get funding to do that. But somehow you do need to sort it out between you.