With a couple of kids, you do want the most possible seating / floor space. However, you should not focus on 9600 lb tow capacity. That number is marketing hype. It is considering the driver has no cargo, no aftermarket accessories, no passengers, and he weighs only 150 lbs.
Your true tow capacity is limited to the truck's weakest link in it's various ratings. That weak links is your payload. Probably, a similar statement in your owners manual.
Examples:
------------------------------------------------------------------------------
Manufacturer numbers
9600 lb tow capacity, 7100 lb GVWR, curb weight 5650 lbs
7100 minus 5650 = 1450 lbs payload
9600 lb trailer with 12.5% tongue weight = 1200 lbs tongue weight
1450 payload minus 1200 lb tongue weight = 250 lbs available for driver and a 100 lb hitch
------------------------------------------------------------------------------
Real world numbers
9600 lb tow capacity, 7100 lb GVWR, curb weight 5650 lbs
7100 minus 5650 = 1450 lbs payload
1450 lbs minus 100 lbs for dealer added accessories (bed liner, floor mats, etc)
1350 lbs minus 200 lbs consumer added accessories (tonneau cover, fiberglass cap, step bars, etc)
1150 lbs minus 500 lbs of people = 650 lbs payload available for hitch and tongue weight
Divide 550 by .125 (12.5% tongue weight) = 4400 lbs loaded trailer
-----------------------------------------------------------------------------
You need to figure out your real world number, for available payload, and shop accordingly. Towing at or above max weight can be quite unpleasant.