Thanks guys, that gives me a bit of a start.
I guess I was assuming that the hitch on the truck was the WD system (since the sticker lists "Weight Distributing" on it) so now things like tension bars, etc make more sense. I think my uncle towed the trailer up to the summer grounds for her so probably no chance of getting that system. I'll look in to an Equal-i-zer or Reese Dual Cam.
So for brakes, I need to have my dad check the trailer for a controller (or ask my grandmother/uncle)? Perhaps a dumb question, but how do I know if my truck has a trailer brake controller? Is it one of those things that if you have it, you will know you have it?
The rest of the trailer should be good. Tires are 1 year old and the trailer is kept covered and out of the elements. I've already got my parents doing all that checking, though.
The 3.5L Eco's are strong trucks. I don't have much worry towing around the flatlands of Texas down here, but I'm highly anxious about towing it down from 10k' elevation to the ~200' elevation here. Not really worried about fuel mileage as that is expected to be well under 10MPG. It's more the downhill and distance that is worrisome to me.
So to sum up:
1) I need to get a weight distributing system with sway control installed on the truck (Equal-i-zer or Reese Dual Cam).
2) I need to have the trailer checked for brake controller (and probably have it tested).
3) I need to check the truck for a brake controller and get one installed if I don't have one
4) General/routine check on the trailer (tires, wiring, all the usual sort of stuff)