We stayed in Porto Vecchio on the Corsican east coast which was lovely. There are a couple of fabulous Caribbean standard beaches just south of there with camping nearby. I adore Venice but it will be busy in the summer and wouldn't be my first choice if you have a young family.
Got to say we found Corsica quite expensive so with exchange rate now will be worse. An alternative would be west coast of Sardinia which has gently shelving beaches, great food and is less windy than the north-east coast.