Your post brightened my day! Just the thought of Sanibel made me warm up on this cold day:)
My husband's family has vacationed on Sanibel Island since the late 80s. They own 2 weeks of timeshare at Casa Ybel. I have vacationed with them there since the mid-90s. We still go every year--last 2 weeks in July. My husband started going when he was in middle school and now we bring our 3 boys (5, 2, and 6 months)
Casa Ybel Resort is great. It has time share units and rentals. Our place is a 2/2 with a full kitchen. It is RIGHT ON the beach. You do not want to stay anywhere not on the beach b/c parking is bad. Casa Ybel also has a great kiddie pool. It's definitely one of the nicest resorts on the island.
http://www.casaybelresort.com/
There are a couple grocery stores on the island (Jerry's is one), but they are kind of expensive. Once you're on the island, you'll probably stay on because it's a $6 toll to come on. There is a movie theater, Dairy Queen, and plenty of restaurants and cute shops. If you stayed at a place like Casa Ybel, you wouldn't have to leave!
PM me if you have more questions!