An Executor is the person appointed in a will to wind up the estate in accordance with the deceased's wishes. An Executor may also be a beneficiary, but not necessarily so. Is your husband the sole Executor and sole beneficiary of his father's will?
Where a property is involved, Probate will always be required. Before he can sell it, the property will first need to be transferred to your husband. Although the two transactions could take place simultaneously, the transfer to your husband can only happen as part of the overall administration of his father's estate. All the assets and liabilities will need to be taken into account in order for an application for a Grant of Probate to be made. It's at this point that an assessment for inheritance tax will be made. If such tax is payable, it needs to be made at this point (i.e. before any assets are sold), so it's often necessary for a loan to be taken out by the Executor(s) for this purpose. Once the Grant of Probate is obtained, any liabilities of the estate (including any loan for inheritance tax) must be paid before the assets are distributed to the beneficiaries.
When you say that dh's mother has signed over her interest in the property, what exactly was her interest? Was she a joint owner? If so, there are two ways in which the property could have been held - jointly, or as tenants in common. If the property was held jointly, it automatically passes to her and will not form part of the estate. That's good in a way, as it will probably mean that the estate won't be big enough to attract inheritance tax. I can see a couple of potential complications, though. If mother gifts the house, capital gains tax will be payable on a sliding scale if she dies within 7 years. How are her nursing home fees funded? It's unlikely that she would be able to give away an asset and then rely on the State to fund her care.
If the property was held as tenants in common, father and mother would each have held a percentage of the property which they can bequeath separately in their wills. This is common where divorcees or widows/widowers, each with their own children, re-marry and buy a property. What would then normally happen is that the surviving spouse would remain in the property until their death when the property would be sold and the proceeds distributed in accordance with the individual wills.
Even if the property was vested in father's name alone, mother would have an equitable interest. Whatever her interest, it would have to be transferred legally.
For both the Probate and the transfer of property, your husband is going to need the services of a Solicitor. Whilst I understand your desire to tie things up quickly, there is a process which has to be followed and it's likely to take months, rather than weeks.