If a child gets paid to care for elderly parents in the parents home, does the child have to claim the payment as income?

It depends on how old we're speaking of when we mention "a child". If the child is a minor, then the child does not have to technically report it as income if under the age of 16. From ages 16-18, this can become tricky depending upon whether or not the child taking care of his elderly parents is considered "employment income" for tax purposes. If the child is receiving benefits from the State of Michigan or third-party to take care of his elderly parents, then I would say that that money is taxable income and should be reported. If however, this money is paid as a mere allowance, and not in exchange for hours or duties worked, i.e. employment, then no, this money does not have to be considered "income" for tax purposes. I would speak with a local tax attorney in your area for more specfics regarding your situation.