I plan to move with them to be their caregiver. My mother shows signs of dementia. My mother is originally from the state they plan on moving to and she really wants to move back. I feel it is a good move because I will eventually need more help caring for them and my sister lives there. Many people have told me it's not a good idea because her symptoms could worsen or she would be confused. I think it would be beneficial because she misses my sister and she becomes depressed. If she was being moved against her will or to a care facility then I can see where it may not be a good move.
I think a key mitigating factor here is that your mother will continue to be with her husband and with you. Her bedroom may not look the same, but she will have the reassurance of familiar faces. Also she is the one who is wanting this move and to be near your sister. It is always a crap shoot, but I would guess this move could have a good outcome.
Is your father in favor of this move? Is he retired? Does he know people in Mom's home area? Will he be leaving a support group behind? Being the spouse of someone who has dementia is life-changing. Be sure you consider his needs, too.
You might also consider the service levels of the two states. With dementia the patient needs increasing levels of care. What is available in the two places?
Are you retired? Are you financially prepared for your own old age? Can your parents pay you for the care you provide?
There are lots of factors to consider in a move. As far as your mother's dementia is concerned I don't think anyone can give you a precise and guaranteed answer. My personal take is that the dementia is not a stopping factor.