Hi vucko....just my two cents....I often go in June because I love off season. But to be honest it is HOT HOT HOT. So if you are used to A/C then I would recommend that you get a place with it. I stay on the cliffs and with the sea breeze and a strong standing fan I am OK. Pool with kids is always a good idea. Stay in the shade when you can, pace yourself and drink plenty of fluids (water type that is in the heat).....don't go hiking in the midday sun (lol) and you will be fine. Low season there is a bit of a decrease in vendors but in my expereience you can get anything you want no matter what month you visit.

Its so cool you are exposing your young ones to the Carribean. Enjoy your reache.