Here's what I told my daughter:
Hook up the trailer and drive it out into a field or pasture with rough ground. IOW, simulate an emergency stop in a rough barrow ditch (that's "bar" ditch for you Texans). Then change a trailer tire by mounting the spare on the ground and the "flat" in the spare tire carrier. Then be certain you load everything you used to change that tire back into either the truck or the trailer. Jack(s), lug wrench, any other wrenches. Did you use a base for the jack, such as a big piece of plywood or 2x lumber? If you did, then be sure that jack base goes with you. A floor jack makes changing tires easier, so if you used a floor jack, that floor jack goes with you too. (I always haul a full-size floor jack and a 2'x4' piece of 3/4" plywood as my jack base when towing on long trips.)
Next, change a tire on the truck by mounting the spare on the ground and the "flat" tire in the spare tire carrier. Then be certain you load everything you used to change that tire back into either the truck or the trailer.
I drive newer tow vehicles that will not likely need spare parts such as water pumps and fan belts. But if your tow vehicle is older than about 3 or 4 years, then do research to determine what is the most likely parts to need replacing before you get home, and take those spare parts with you - just in case.
When I first replace a fan belt on a new tow vehicle, the old fan belt goes in the spare parts area (behind the back seat). It may be on its last legs, but it will probably work until you can get to a place where you can buy a new fan belt.
Before you leave home, complete all routine maintenance that might come due during the trip - oil change, coolant change, ATF change, brake pads, shocks, brake fluid flush, replace fan belt(s), trailer brake shoes, etc.
Grumpy ole man with over 50 years towing experience. Now my heaviest trailer is a 7,000-pound enclosed cargo trailer, RV is a 5,600 pound Skyline Nomad Joey 196S, and my tow vehicle is a 2012 F-150 EcoBoost SuperCrew.