Until I saw your budget I was going to say Hawaii (but you might win lotto, so it could be a possibility) they love kids there, it's hot and, you can get as many poolside drinks as you want.

We went to Port Douglas in November. It should be nice this time of year. The place we stayed at had an amazing pool but I wouldn't recommend it if you have escape artists living with you (as we found DS2 playing in the pond out the front at 2am one morning) and I don't think they have a kids club.

Have you thought about Fiji? I think most of their resorts have kids clubs.