The cost of housekeeping services are never a deductible medical expense; only personal care services may be deductible under certain conditions. However, the cost of housekeeping services incurred to enable you to work may qualify for a dependent care tax credit. To be eligible for this credit, the nonworking spouse must be physically or mentally incapable of self-care. Whether your wife meets this condition is up to your doctor.
The legal transfer of property, rights, or interest to another person called an assignee. You cannot avoid tax on income by assigning the income to another person.