Shawn,
Welcome!!!
Unfortunately though as it has been mentioned you will be very, very limited on trailer choices if you go with the Expedition!!! For the majority of 1500/150 trucks and the advertised "tow rating" is useless. As mentioned look for the yellow sticker in the drivers door jamb that states the payload for that truck/suv. This amount is the max payload per the manufacture which includes: all passengers, all cargo (coolers, bikes, firewood, etc), any accessories added (step bars, mud flaps, truck cap/topper on truck bed, etc), the wdh (weight distribution hitch), and the tt tw (travel trailer tongue weight). While you have 3 younger kids now, they will only continue to grow, which equals more passenger weight.
Check this thread out, it has a ton of info regarding what you will be up against. While it is a different tow vehicle, it all comes down to payload.
Realistically I would think your only option if you want a new vehicle is to look at a 250/2500 or 350/3500 van. This will give you the seating capacity you need, and the payload you will need for a large enough trailer. Used there is the Excursion or a 2500 Suburban. Though the Burb is limited on the newer models to 1000lbs tw due to the hitch.
The other option may be taking a second vehicle for most of the passenger, though not very practical.
Good luck!!!
