Inquired about a Medicaid "bed" for my Mom in NC and was told she makes $2.00 over limit. Recourse?

My Mother (87) has Alzheimer's. Granddaughter moved in for overnight care and we pay a caregiver a few hours each day. She resents the granddaughter's presence - when she knows her - and said she'd rather die than go into a home. Have been told the only two options are private pay at $4000-$5000 per month or that she should qualify for Medicaid assistance at an assisted living facility with 10% Medicaid beds.
She's not able to take her meds, is not toileting properly or bathing properly; does not eat unless told to do so. I am several states away but will apply for guardianship and power of attorney. Everyone says she is in a gray area; with $2.00 too much income per month to qualify for Medicaid, but no assets other than her home to help pay for assisted living or nursing home. Any ideas about a possible re-evaluation by the Medicaid office??