A few options in May:
1) Sicily, either Marsala-Trapani area (beware Stagnone is perfect for kiters but not so good for non-kiters... after all is not an open bay but a lagoon, I wouldn't advise for non kiters) and Pozzallo. You could stay at Floripa kitehouse which is 30m from the spot, and the beach is white and wide. This would be much better for your family, and if you could rent a car, youl could also visit Noto, Modica, Scicli and Ragusa... believe me Noto baroque Cathedral is really fantastic!
2) Sardinia either North and North-East (Porto Pollo, San Teodoro, Siniscola) or South-West (Chia, Porto Botte, Porto Pino, Punta Trettu). All of these are very windy, beatiful (and warm as well...). Better if you could rent a car and make a short tour. Look for the other post related to Sardinia.
3) Puglia, with Northern winds, if the summer resort aren't still working, you could probably be allowed to kitesurf at Porto Cesareo... unique!
3) Croatian coast, Neretva area. I've never been there but I've been told to be really beatiful and fit for kite.
4) Greece in May could be really lovely, but in May you won't find the reliable meltemi wind which make the Ciclades (Rhodes, Paros etc.) a paradise for kite in Summertime. But Ionian coast could be better, and Lefkada would surely be a good choice!
5) Southern France, Hyeres and Beaduc are well renowned spots and surely quite warm
6) As Toby says, Red Sea in May is perfect and really windy ... it's not actually Europe!