Newbie and can't figure out the "What can I tow" math

You will be at or a little over the payload rating with the tongue weight and the family, meaning any significant cargo will need to go in the trailer.

As for the 8400 lb tow rating, keep in mind that a TT with its high walls presents a lot more wind resistance than a boat or an open car hauler, or even an enclosed equipment trailer. That's why everyone is talking payload as the limiting factor.