Sanibel island on the gulf coast would be perfect for you. Lovely beaches (some of the best in world for shells), low level development, huge nature reserve, loads of cycle paths all over island. Very family friendly and relaxed. Stay gulf side, not overlooking mainland- it's prettier and has magnificent sunsets. Westwind Inn is lovely and I imagine there are lots of self catering options too, if you prefer that.
We are planning a 2 week holiday with friends to Florida in 2016, plan is to stay in separate villas in Orlando close to each other, never been before. We have 2 boys but are not fussed about Disney, plenty other stuff planned. But me and DH would also like to "explore" a bit and maybe separate the holiday into 2 ie a week in the villa and then a week elsewhere. So need some ideas for the second week, we like relaxing to so beach resorts look good, I had thought if driving from Orlando to Miami for a few nights and then onto a gulf coast beach resort for 5 nights. Does anyone have any experience, ideas etc?