Sounds like you need an estate attorney. You move some things around to keep the state from getting to it, however, from my reading, it would seem that any OBVIOUS manipulation to avoid paying for the services would leave you open. Estate attorneys will be able to tell you how to protect the assets from going to the government.
The better question is who should pay for her care? I'm sure going to take some heat for this one, but personally, it shouldn't be the Georgia Taxpayers that should pay for your Mother. If she has an estate it should be sold to take care of her. Actually, if she has an estate, it's likely that she could afford to live in a much better facility than the state run ones.
Good luck either way.
Tough questions. My mother-in-law once owned a retirement/assisted living facility in Monroe, Georgia. More than once, I recall her discussing medicare/medicaid, family contributions etc. These questions are really outside the realm of a Realtor. I suggest you make some inquiries from other sources, such as an attorney or perhaps speak with the care providers manager for more insight. I do think that there is a time frame (in years) that comes into play if all assets are transfered and then she becomes, for lack of a better term, a ward of the state. Good luck to you and your family as this is not an easy transition many times. Oh, on a side note, once the decision was made, most of the women I met were very happy in their new space. They made friends, had places to go and people to see!