[JRTJH]

I believe the 2011 F150 with 3.5l EcoBoost engine was available in 4x2 and 4x4 versions equipped with either 3.21, 3.55 or 3.73 rear end versions. Each is a significantly different vehicle and each will have significantly different tow capacity. The limiting factor for most F150 trucks is not the capacity of the driveline to mechanically pull that size trailer forward. The limiting factor, for most is the ability to remain below the payload, GVW and rear axle capacities of the truck. The owner's manual stipulates staying below ALL of the capacities. Many (well some) people advocate that if you're OK on any one, ignore the other capacities. It really comes down to whether you want to put your family in a truck that's at/over the factory specified limits.

I'm guessing that with your truck, you'll be overloaded once you put cargo/camping gear/passengers in the truck and hitch a loaded trailer to it. The tongue weight for that trailer will likely fall between 650-950 pounds (10-15% of trailer weight). Also keep in mind that currently you list 585 pounds for family weight and 100 pounds for bicycles. Remember that next your your kids will weigh more than this year and the following year, more again. Additionally, the toys they want will change from 2 bicycles to 2 dirt bikes to 2 ATV's and they will, in the near future, want to bring friends along or they'll pitch a "hissy fit" to stay home..... That "family weight" will only get larger, maybe even with every trip.