I've been to Sanibel many times, but I have never really noticed any good beer stores there. To tell the truth, I've never really looked while I was there. There are two supermarkets, Jerry's on Periwinkle and Bailey's on Tarpon Bay Road that have liquor departments. Huxter's on Periwinkle also sells beer, but I don't know if they have anything other than BMC there.
The best beer I have had in a restaurant there was a Key West (well, acutally it was two, but who's counting?) at Doc Ford's.
There used to be a brewpub on Sanibel, but unfortunately they closed a few years ago. Hope you enjoy your trip!