Tools
I'm always interested in this topic, especially on the motorcycle forum which I follow. Some riders take a full tool set, so full in fact that they must have a sidecar to carry everything! On the other side of the coin, other riders say they only need two tools......a cell phone and credit card! I guess they are both valid approaches!
I'd add that you should check to be sure you can change a flat on your trailer. I carry a spare jack and lug wrench in the pickup bed so I don't have to disassemble the truck interior to get to these necessities, regardless of whether the flat is on the TV or trailer. This is especially useful as the truck interior is usually loaded with other items. With a dual axle trailer, you can forego the jack and use a Trailer Aid ramp device to get the flat tire off the ground.
Also, we once had a trailer and the lug wrench wouldn't loosen the spare tire. The lug wrench was the right size for the nut holding the spare, but the nut was a few inches down on the bolt, and the lug wrench would need to have a very deep socket in order to work. So, I had to always remember to carry my socket wrench with a deep socket and an extension.
A "dry run" on changing a flat, while in the comfort of your own driveway, can be a valuable experience!
You might also find use for a Robertson screwdriver. The Robertson screw is the screw that requires a square bit. Many RV manufacturers use the Robertson screw. There are 3 or 4 sizes, I believe. If you need to do some interior repairs, or even remove the wood trim so you can lube the cables on the lift mechanism (which should be done at least annually) you'll find a set of Robertson screwdrivers to be of use. You can also buy one screwdriver with interchangeable bits, which would save a bit of space and weight.
Always have a can of WD-40 or similar to use on the stabilizer jacks, tongue jack (whether electric or manual), hitch coupler, door hinges, and other miscellaneous places.
Safe travels,
piperjim