Medicare and Medicaid serve two very different purposes: Medicare is similar to regular health insurance, providing coverage to people over the age of 65. Medicaid, on the other hand, is
basic health insurance for people older than 65 who have limited income and assets.
If your mother requires skilled care, Medicare will cover rehabilitation and nursing home care. However, it won't cover custodial or intermediary care. For example, it won't cover an at-home health aide unless one is determined to be medically required.
To get Medicare coverage for nursing home or rehab expenses, your mother will have to meet certain requirements: She must move to a nursing home within 30 days of her hospitalization, and she must have initially stayed in the hospital for at least three or more days.
If she meets those qualifications, Medicare will cover 100 days in a nursing home. The first 20 days are covered in full with a $124 per day co-payment for the next 80 days.
As for Medicaid, it does cover custodial and nursing home care -- for those who are in financial need. This means that your mother would have to spend down her assets to roughly $2,000 (depending on the state she lives in) before she could qualify for the program. Once she qualified, the cost of a Medicaid-approved nursing facility would be covered. However, whatever income she received would automatically go first to cover the cost of the nursing home.
Unfortunately, just because a facility is Medicaid-approved doesn't mean that it will meet with the approval of you and your mother: Medicaid-approved nursing homes aren't always the best option in terms of quality care.