It would be a hard find to go 4 days to southern. Most sountern's start in Puerto Rico and go at least 7. You may be able to find one out of Aruba, but I doubt it. If you are looking for a 4 day, you'll need to sail out of a US port (most likely).
I have sailed on 12 cruises (non-disney) and LOVEd them all. NCL,
RCCL, Dolphin, Aloha Pacific, CCL, Windjammer. Each different, yet the same. Each company has their plusses and minus's. We've never had a bad cruise and I'm sure which ever you choose you will enjoy.
With Grandma aboard, I'd stay away from Carnival. Can get loud, rowdy and crowded. Celebrity is supposed to be nice, but haven't had the pleasure...YET! I'd say take a look at the itinerary if that is important to you. If gambling is, then look at the ship with the larget casino. If Rest and relaxation are your thing, look into an itinerary with a lot of sea days.
There are sooooooomany opinions out there, the only way to know what you like is to give it a try.
Mrsfuzzmo