Basically a POA does not five Sis control over Mom--so long as Mom has a lucid moment Mom is verly likely free to just alk out of the facility and ride back to MS with you, and if Mom is semi with it she can revoke the POA as well.
The thing to be very careful about is a POA probably gives its holder easy and relatively unchecked access to the grantors assets/income and they may well be able to clean out the larder.
Moral issues aside, if Mom is headed for long expensive care, there may be prudent ways to clean out the larder as quickly as possible. The folks who were getting Medicaid were getting about the same level of care on the same floor, same building, same staff as I was paying at $8000 a month for care of my MIL--
If Mom wants to move, the quicker she does so while she has more of her wits about her, the easier it will be,
Again, I caution you about POA's who clean out the larder.