Jumeirah Beach would be fun for the kids. There is a small admission fee. Also, while I'm not a fan of malls, Dubai Mall has some play areas for little kids. And, of course, that would be air conditioned (a big plus in May). Outside they have the Belligio-like water show -- that'd be good in combination with an early evening dinner.

Then again, maybe you should find a hotel with its own beach. Others here might have ideas on that. One more idea: boat ride on The Creek.

This isn't a great place for kids, but you can make it tolerable for a week.