Hi and welcome! If anyone can help you find the right vehicle to be safe, it is this forum!
Here is the short answer..
Your trailer ready to go will likely have too much tongue weight for an Expedition receiver. You MIGHT be able to use a better aftermarket one as long as it does not cause you to exceed payload and axle ratings. Best thing to do is pack the trailer and use something like a sherline scale to weigh the tongue, you will know exactly what the tongue weight is.
There may be SOME F150 out there that can tow it, but you must be carefull and really know what you are looking at. F150 comes in many variations and can have payloads from 1200lbs to over 3000 depending on configuration. That trailer tongue weight plus family is going to require at least 1650-1700lbs of payload depending on how many people.
Your trailer is really on the edge of 1/2t towable, some can most can't. 6500lbs loaded seems to be the 1/2t sweet spot, there is no way you will be 6500lbs loaded if it is 6000 dry.
Turn key solution is a 3/4t truck or 1t truck or van. It will have the payload and receiver as equipped to haul your trailer.
How many people will be traveling?
2007 Expedition EL 4x4 Tow pkg
1981 Palomino Pony, the PopUp = PUCampin! (Sold)
2006 Pioneer 180CK = (No more PUcampin!):B
Me:B DW:) and the 3 in 3 :E
DD:B 2006, DS 😛 2007, DD :C 2008