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Absolutely - yes - these are deductible medical expenses.
Please see for reference IRS publication 502 page 12
Nursing HomeYou can include in medical expenses the cost of medical care in a nursing home, home for the aged, or similar institution, for yourself, your spouse, or your dependents. This includes the cost of meals and lodging in the home if a principal reason for being there is to get medical care.
So far - because the PRINCIPAL reason for your wife being there was to get MEDICAL care - all related costs are deducted as medical expenses.
Let me know if you need any help with reporting.