The hitch will likely take about 100lbs off of that number as well, leaving 500lbs at most for cargo/tongue weight. Assuming you family like to take a few games, books, food, etc.. I would plan on a TW of 450lbs to be safe. That's leaves you with a trailer that is in the 3,000 - 3,500lb area, once loaded.
The only way to increase your capability is to get a 3/4 or 1 ton truck.
If you look at the 26BKS in my sig, it weights about 8200 loaded for camping which is a lot heavier than sticker, and when the batteries where still on the tongue it had over 1350lbs of tongue weight...
I am sure a empty 1/2 ton would be rated to tow a trailer that big, but having towed it with an upgraded 1 ton I sure wouldn't want to.
Airbags add stability and load leveling, not capacity.
Anti-sway bars and shocks also add stability, but no capacity.
Better tires add stability, and a safety margin but no capacity on a 1/2 ton (might on a 3/4 or 1 ton thou).