Have you considered Tuscany? Kids seem to love it, it's full of attractions, outdoor activities and history as well as a nice coastline.
I would try to go in the medium season rather than high season. Somewhere beginning of July or earlier, or after August is best, as the weather will still be nice, but villas will be cheaper.
I've actually helped produce a guide to Tuscany for children (http://www.to-tuscany.com/local-tuscany/tuscany-for-children/) that lists some great things to do for all ages. There are some coastal villas on that site as well, but I'm not sure they are close enough to the coast for you - about 13km?