You are forgetting your payload. The truck will have a sticker in the door listing max payload available. That's the total weight you can carry inside the truck. Large SUVs can be all over the place on this, but many have a smaller payload than their full size PU truck equivalents.
Your tongue weight which, if you maxed out the trailer weight, at 13% would be 988#. Then there is the weight of the WDH hitch itself, often reaching 100#. So if your payload is generous and it's 1600#, the tongue and hitch leave 512# in the truck. You are saying your family and "stuff" is 800#. That puts you 288# over your payload.
I'm thinking you'll need at least a 3/4 ton truck to make this work. I can't comment on travel with a family in a crew cab PU, but I know there are those here that can.
I wish you the best!
