This rather looks as if your ex or her solicitor don't know what actually happened. Your father owned the business (but only a lease on the shop). He did not make a will & under intestacy laws your mother would inherit a limited amount (I think �125K) & anything else she would probably hold on trust for life for you & your siblings (if any).
So it could be they are assuming that assets (including the house) were left to your mother under the intestacy & are therefore in trust for you.
However, from what you say there were a lot of debts left by your father so I assume the net estate value would have been low or nil. In which case there is no trust. Also, they obviously have the wrong house!
I don't know whether the solicitor you spoke to is acting for you, but I don't like the implication that you don't need to do anything. If nothing is done the Court will accept what they have been told - however erroneous it may be. You certainly need a solicitor to write back giving the true facts & - hopefully - get the Court application withdrawn.