You need to see an elder law attorney ASAP to get the agreement documented. They can also assist with the tax implications. If not done could have significant effect on his health care in the future!
It depends on how you word it, if it is rent, that goes on a Sched E. If it is lost wages, then you have to do quarterly withholding and send it in. If you are an "independent contractor" you get a 1099 and list it as miscellaneous income on the 1040 and fill out the FICA forms. You carry that information over to the Ohio return and pay the state taxes on it.
Recent lesson I have had as a result of trying to negotiate a care agreement is that a family in home caregiver will not pass Medicaid scrutiny as an "independent contractor". Not sure why at this point. In addition the taxes, FICA, employer and employee portions will significantly reduce the $3,500.00. See an elder law attorney.