The denial letter should be very specific and you need to sit down with the nursing home and get them as the representative payee. It will save you a lot of headaches down the road.
Example: She went into the nursing home Jan 1. Since she gets $1290, all but $30 would have to have been paid to the nursing home = $1260. She only gets to keep $30 a month for personal expenses. You need to prove that is where the money went. It's a whole lot easier to just make them the rep payee and let them worry about the financial reports.