Maybe Tampa, FL?
Clearwater Beach is soft white sand with the Pirate Boat and Clearwater Aquarium to see Winter.
Busch Gardens is great for kids that age. Lots of rides for the little one. There is a whole play area for the 4 year old. Jungala is amazing for the 10 year old. Plenty of animals to see amongst the rides.
The Tampa Zoo if great. They have some small kiddie rides, a water spray area, camel rides, really fun for kids.
The Tampa Aquarium awesome with an outside water spray park for the kids and a Tiki Bar for the adults included in your ticket price.