I drove from the Bay Area to here with a 20 year old and 3 cats. I did sedate the cats the first day of the trip, nothing after that. I was the only driver as I rented a car for the drive -- wanted something a tad larger than a Miata for this trek. It really wasn't a bad trip. Actually, it was fun -- we meandered a bit to stop where we wanted, when we wanted. The only proviso was that we had to be in TV the morning the mover arrived (we made it, barely).
However, everyone was relatively young and healthy for this jaunt. Would it be possible for your mother to fly alone after you arrived here? Have her stay with friends who could put her on the plane and you pick her up? I agree that cats and planes don't mix well -- plus I hate the idea of animals being in holds .. just too many risks and I don't think there is any airline that will allow you to take a pet into the body of the plane anymore.
If you decide to drive, you might want to check out
www.petswelcome.com -- they have a list of hotels/motels/b&bs that allow pets.