How big are you and kids? If I take my spouse, myself and 2 of 4 smallest kids, or two biggest as teens, I have 800-900 lbs of people, Add into that the 150 lbs of hitch, 3000 lbs of hw, plus other assorted odds and ends, I am over 4000 lbs of payload needed. I should also point out, I pulled a 6500-7000 lbs TT with my family of 6, 2 alaskan malamutes, rack, canoe etc, and was typically 200-800 over the manufacture gvwr, but below ALL axel limits, and most importantly, the registered gvw of the truck. with NO white knuckle driving experiences just driving...
BUT, with this said.....a dually may be the better option if you are going to put bikes in the forward part of the bed, maybe a generator etc. You could easily need upwards of 5000 lbs of payload.
Marty