Hi, I'm responding because you asked about Sanibel and Ft Myers.
We're going to Sanibel later this month, we've gone every year since I had kids. I can personally recommend Sanibel Beach Club I, II, and Shell Island. I own a unit but use mine every year; there are sometimes rentals available if you call the office phone numbers. All three resorts are in a row at the lighthouse end of the island (very, very laid back and bike-able). They have outdoor pools and are very family friendly: small playgrounds on site, bikes and board games to borrow, tennis courts with racquets to borrow, boardwalk access to the beach, sand toys available to borrow, towels available to borrow for a deposit (you get it back when you return the towels at the end of the week). You don't realize how much room in your suitcase beach towels can take up until you try packing them with diapers and kid gear! :) It's really nice not to have to bring them!
The units are two bedroom, two bathroom with full kitchen including all full sized appliances, a dishwasher and a washer & dryer. There are screened porches so you can enjoy the evening without mosquito bites and there are grills on the grounds so you can "cook out" if you want to. We love it. All the linens and dishes are already in the unit so you just buy your food and paper napkins and you're ready to spend the week.
Other than the obvious attractions of the sandy, shelly beach and the pool, Sanibel has the JN Ding Darling nature preserve, where you can look at wildlife from your car on a drive-thru trail and also view some neat things and a movie in the visitor center. Our son (nearly 4 now) loves doing this every year. There is a ton of shopping on the island, and in at least Periwinkle Place and the Jerry's (grocery store) Plaza there are two shops that sell toys and fun kid things, there are probably others that I'm not thinking of right now. Jerry's has a lovely courtyard with lots of caged tropical birds like parrots that are fun to go look at and some of them even talk to you. Mango Bay (a store across from Jerry's) and Bailey's General Store have a lot of fun kid stuff, too.
If you get sunburned it's fun to wander around those shops for an hour or two and give your burned shoulders a rest from the sun! If you go into Ft Myers there are a bunch of places to visit, like historic houses and mini-golf and I think a kids museum, but my kids tend to just want to keep going to the pool every day and enjoying the resort, so even if I've been to them myself, I've never tried them with my kids!
The tennis courts are fun with a 2 year old, as long as you're ok with continually retrieving the ball for them and just laughing as they hit it all over the court for you. Borrowing the resort bikes (or renting them from Billy's Rentals) is a great way to spend a morning; you can either rent a trailer and tow the little person along behind you, or you might get lucky and get one of the adult bikes that has a kid seat attached on it. We love biking down to the ice cream & coffee shop (Sanibel Beanery) where they have amazing cake, sharing a piece and biking back. On Periwinkle Way about halfway down the island there's a really nice (and big) playground that you can bike to and then bike back, too. The bike trails on the island are nicely maintained so it's easy to ride even if you don't do it often at home. (We don't.)
We use the kitchen to eat almost every breakfast and about half of our lunches and dinners over the course of the week. The rest of the time we have fun with eating out. Great places to try with a 2 year old include... The Bubble Room (very kitch, very fun, but also a bit expensive. Leave room for dessert, it's amazing). Matzaluna (pizza, pasta, and they're super nice to kids). The Island Cow (think island style diner food) which often has live music at lunch and dinner (not too loud, like a single guitar player singing). And it sounds unlikely, but Doc Ford's sports bar features really excellent food, not just the usual bar fare and they have a kids menu and are very welcoming to children. Plus, the noisy-ish atmosphere means nobody will notice if your kid is a little louder than normal after a long day of sun! Also Pinocchio's Ice Cream is pretty delicious and walkable from the resorts I mentioned.
And if your child requires more entertainment, the Bailey Shell Museum is pretty cool, there is community theater on the island which may or may not be running a show while you're in town, and there are always boat tours running that can take up an afternoon. If you're willing to drive down to Naples there's a zoo. Whew! Hope this helps. If you decide to go down to this area and need any other info, feel free to contact me.
Have a great vacation, where ever you wind up.
