You would have to have the trust reviewed to see if it qualifies for a reverse mortgage, not all of them do.
If the trust does qualify for a reverse,
and you and she decide to go that route, choose your lender carefully.
A reverse mortgage would become due and payable upon her moving out of the home for more than 12 months due to medical reasons. The lender cannot take the home, but you would have to pay off the balance owed on the reverse.
One of the options on a reverse mortgage is taking the loan proceeds in a Line of Credit. That way she can tap into the money as she needs it, instead of borrowing it all at once. That will help to preserve equity for you and your brother.