Congratulations on your upcoming nuptials and subsequent kite holiday... er, sorry... honeymoon, indeed! (Did you really have to get married to go on a kite holiday?)
Summer in the Caribbean means Trade Winds!!
You can consider Cabarete, which has amazing wind in the summer! There are now beautiful accommodations availble just steps from the beach- both you and your bride will be happy! Luxury accommodations, privacy, security, pools, concierge services... great kiteboarding, restaurants, nightlife, surfing, horseback riding... Or, just relaxing under the sun.
You may also think about St. Croix. Beautiful water and lots of kiteboarding possibilities. It is much more quiet than Cabarete, but this may be more of what you would want. Downside is that there's not much to do where you'll be riding, whereas in Cabarete, you can ride and she can hang out or shop or do her thing right there in the same area. Here, there are very nice hotels or houses available.
There are other places, too, of course...
If I can help you with anything- planning your holiday to just simple questions, please send me a pm and I'm happy to help!
Happy New Year!