Which state pays benefits?

My mom called me and we arranged for me to move back to my home state to financially assist her while she went down south to care for my aunt. While there, my mother developed dementia and stopped eating and my aunt began to care for her. My mother is retired and her address still in our home state but we don't want to physically move her back because she is comfortable and wants to be buried down south. Since her Medicare is in one state but she is being cared for in another can we still get caregiver pay to my aunt, who is taking care of her? Which state would authorize this? My mom has Medicare and she would qualify for Medicaid because here Social Security income is so ,but which state would handle the payments?