What are your must haves for a travel trailer tool kit?

We just bought a small one and are planning a long trip in it next month.

AAA with RV+ in your wallet is a good start.

Is good Sam or aaa better?

You'll need an air compressor and a jack that can lift the trailer.

https://www.boundarywaterscatalog.com/gransfors-bruks-inc/grnsfors-bruks-small-splitting-axe-5763

https://www.harborfreight.com/2-1-2-half-ton-trailer-stabilizer-jack-96406.html

It's not a necessity, but a battery powered drill with a socket will make lowering and raising the stabilizers quicker. Just don't go too fast or use too much torque on them. A floor jack will make    lifting the trailer up to change a flat easier also. Take a piece of plywood or something similar to put under the jack on soft ground.

I don't know anything about Good Sam, so this is not meant to make them sound bad. I have had AAA RV+ for years. I only used them once for an actual RV. I had a 4 door F350 dually with an 11.5 ft. overhead Lance camper on it and blew a transmission line going to the trans. cooler. They sent a wrecker big enough to pull the whole rig to a mech. shop with no problems. BTW, when a transmission line breaks and throws trans. fluid over a hot engine, it makes you wonder if the whole world just caught on fire. Thankkfully it didn't in our case.

Aside from the customary screwdrivers and pliers, a pair of Vice-Grips is very handy.

So is a bag of zip-ties - there are a million uses for them!

I also carry a cheap digital multimeter - very useful for troubleshooting both 120 volt AC and 12 volt DC problems.

All of my tools ride in the tow vehicle, so they're also useful when the trailer isn't nearby.

The easiest way to figure out what you need is by looking at your RV/Camper. What can go wrong and how would you fix it?

I carry a set of sockets and some wrenches plus the above "normal" sizes for the 5th wheel hitch, etc. A multimeter, small tube of silicon, a tube of lap seal, a roll of seal (forget the name), some spray silicone and PB Blaster. A 4 way wrench for lugs, jack that was fine for the TT we had but may not work with the 5er (have to check that!), rubber mallet, camp hatchet, battery leaf blower, small screwdriver kit with multiple bits, battery op drill and some drill bits, spare water hose gaskets, fuses, electrical tape, duct tape, command strips/hooks and a damn good flashlight/work light. Air compressor and guage,  and check your camper tires + the spare!

Pro tip: if you use a power tool to raise and lower your stabilizer jacks use a drill NOT a impact! Get the 1/4" to 3/8" adapter for the DRILL and use a socket, I think they are 3/4". Set the torque on the DRILL to just past snug on the jack.

12 ton bottle jack, dewalt 20v compressor, 20v leaf blower, 20v vacuum, 20v 1/2” impact wrench, Milwaukee m12 1/4 ratchet, ratchets and sockets, caulk, eternabond tape with roller, screwdrivers, pipe wrench, vise grips, electrical tape, thread tape for leaky hoses, crescent wrench, pliers, nitrile gloves, small electrical repair kit with heat shrink.I’m sure I’m forgetting some things but that’s what I’ve put together for our trips.

Some good lists here.  To add...

Spare shower head
Screen repair roller (esp if you have kids)
Fuses
Some assorted sheet metal screws
Duct tape
Electrical tape
Headlamp

I have a pretty good toolbox full of typical hand tools.
I also bring cordless driver and an impact for lugs though not necessary.
Also carry a compressor but I'm planning to get a high pressure pump because its much smaller and can just be clipped onto a battery if we are out on the road vs having to fire up the generator.
Spares of a lot of items. Carrying a spare AC (air con) capacitor has saved us when we were in a campground with shit power. We only have a surge guard right now but will be adding a EMS to prevent most of that type of issue.
Spare slide motors because I have schwintek slides.
Spare fuses.
Duct tape.
Eternabond tape for emergeny roof repairs.
Pleny of zip ties.
I can't remember what all is in my spares box but if its important and hard to find particularly at night or on Sunday etc. it will save you some grief.
Also carry orange safety vests but have neglected getting road cones/lights/reflectors. Had to change a tire on the turnpike once. It was on the away side or I probably would have just burned the trailer to the ground and left it there. Cars going by 80mph is sketchy as hell.

Does anyone carry pioneer tools? I'm thinking a spade shovel and maybe a mattock might not be a bad idea.

I have those in my truck. Can't do much digging around here without a pick.

I do carry a small camp shovel.
Also carry a pooper scooper and a big jug of kitty litter. We have two large dogs and sometimes traveling makes them have #2 that you cant pick up completely.
There may or may not be a tree saw in there somewhere too just in case.

A spare water pressure regulator, spare end for electrical cord, spare 30A and 50A receptacle, spare fuses and whatever brand breaker you have in trailer.

The spare cord ends and circuit breaker are good ideas.

And pressure regulator

I actually had a leaky hydrant at my last camp and I over tightened with a monkey wrench and broke mine