If patient is already qualified for Medicaid and family wants to transfer her to another facility in same state, will she have to re-qualify for Medicaid?

It does vary by state.  I'd check with her case worker. They will need to be notified of a change anyway. Plus, I'd check to confirm if there is any difference in the level of care. Some places like Special Care units charge different rates. Sometimes, if the person's needs have increased and the doctor can confirm it, they may be entitled to more care/benefits.   I'd get it all confirmed in writing, prior to a relocation though. You're smart to get it straight before hand.

Every state has their own rules so I can only tell you what happened to my mother in my state. She was moved from one NH to another and she did not have to re-qualify.