If family members are paid to relieve the caregivers and at a lower cost, do I report their income? Trying to budget the savings.

Yes. You report the income. And they need to understand you will do so. Anything else will be considered gifting, and should care be needed under medicaid in the two to five year lookback this giving money for care could prevent access to funds. If you are acting as POA all records should be meticulous as to income and outgo from one account. Keep a diary daily as well. And do the tax work at the end of the year.