It's a bit of a labour of love, by the look of it. But if this is what your mother herself wants to do, she has every right to live where she wants and you can but try.
Would she be private pay? Most assisted living facilities don't accept anything but. If so she is free to move anywhere she likes at all. If there is currently however a medicaid component in any of this it is more complex as Medicaid is a joint Federal and State program which has differing rules and applications for every state.
https://www.medicaidplanningassistance.org/transferring-medicaid/
It's a bit of a labour of love, by the look of it. But if this is what your mother herself wants to do, she has every right to live where she wants and you can but try.