There are two issues here. Firstly, there is the conversation between your husband and his parents - namely that the brothers owned the house. Because this is an interest in land, this must have been done by a declaration of trust and the asset would pass under the Will (there would be no need, itwould already have passed under the DoT). It looks to me as if no declaration was ever done and thus it did form part of dad's estate. Unless you can find the declaration of trust and it gives details of the Trustees, I think this one is probably a non starter.
Given that your mother in law is still alive, there is no negligence (assuming the will appoints the aunt and solicitor as executors and trustees). The normal process would be for the property to be transferred to the executors to hold as trustee for the duration of your mother in law's life. Your husband and his brother cannot call for their inheritance while your mother in law is still alive. Their interest only vests in possession on the death of your mother in law.
IF your husband wishes to be bought out, the fairest way of doing this is to obtain an actuarial valuation of the your mother in law's life interest (her life interest has a value too). The purchase price of the property will need to be calculated with that in mind. However, your husband cannot force them to break the trust and it will only be if all parties agree that he could do this. But in my view there is absolutely nothing untoward in the current state of affairs.
Finally, you should get a copy of the Will from the probate registry as suggested above.