I would NOT be concerned about taking taxi's to get the the Dubai Mall. Taxi's are plentiful and that is low season because of the heat. Ramadan will be over the 2nd week of July and things will get back to more normal operation then as well.

Stay at the best property for you..... and take some taxi's.... I would avoid the metro in the summer because of walks adn taxis aren't that expensive anyway........Dubai Mall isn't to be missed and would go multiple days as it has it all. You can go to Burj Khalifa at the top one day, the aquarium for a while, watch the fountains, movies, arcades, not to mention ice skating and shopping etc.

I like the beaches in Dubai as well by the Marina specifically. I prefer the GH for the lounge, but with kids I'd look to the Westin or Le Meridien Mina Seyhai. You will have a great time!