It's my understanding of your facts that the "at home" spouse is the one who died first, leaving the surviving spouse in the nursing home. If the surviving spouse (or the spouse's authorized agent) signs an intent to return home form, the State will probably not consider it an available asset and will not require that it be sold. However, that creates a problem of how to pay taxes, insurance and maintenance on the house. If there is no intent to return home, it will likely be considered an available resource that will have to be sold and the proceeds used to pay for the surviving spouse's care. You should consult a local elder law attorney.The children may be entitled to compensation for their work as personal representative and for work done to prepare the house for sale.
This is state specific so check your Medicaid manual. Each state has its own estate recovery rules. It would be worth a consult with an elder lawyer to see if they can save the house.
This is a situation that never should have happened! Once wife qualified for Medicaid two things should have happened: 1. Get nursing home spouse's name off the deed 2. change the will of the community spouse! I see this often where people did not seek the advice of an elder law attorney, or a good one, when qualifying for Medicaid. As mentioned, the "intent to return home" might work, but more likely you will have to list the home for sale at the Tax Assessed Value. Even then, you still may be able to save assets once it is sold...consult a Certified Elder Law Attorney (CELA) www.nelf.org