I have found after 20 plus years of RV ownership, there are very few "tools" needed when outfitting an RV. I think the difference is, if you are a full timer and don't have a home base to return to. Then, you need to have everything with you all the time and as you have no home-base to return like the week-end trip, or at best a 2 week trip RVer.
There are some things that are an absolute must for me.
1. I must have the jack handle for the stabilizer jacks on the camper.
2. I have a special socket on a flexible shaft that is specific for the electric motors that fit all my slides in the event of slide failure, I can retract the slides manually.
3. This also means I carry an electric drill all the time too.
4. The next item I always have, permanently in the camper, is a socket and wrench specific to fit the anode rode plug on my water heater. It never leaves the camper, as I drain the tank on every return trip home.
5. I also have a specific socket with a 3/4 inch drive and wrench specific to fit the nut for the hitch ball on my Equal-i-zer hitch system.
6. One more thing I have that stays permanently in the camper is a Robertson screwdriver, as all the screws in the camper are Robertson screws.
These items are the absolute "musts" that never leave the camper. After these thing, what I bring is just a wild hair guess, and hope I never have to use them.
I carry in a tool box that stays in the bed of the truck all the time. I call it my RV tool box, but it floats between the house and the truck, or whatever project I'm engaged in. It basically has a flat screw driver, a Philips Screw Driver, a standard hammer, a couple different sizes of adjustable wrenches, a short bolt cutter, 2 sets of pliers, a needle nose plier, a utility box cutter knife, a standard normal pocket knife, tin snips for cutting metal or tin.
In addition, I usually keep in the tool box duct tape, black electrical tape, a few wood screws of different lengths, a small spool of auto electric black wire, auto fuses - the little flat square ones of different amps that is used in both the camper electric panel and the truck electrical system. And that is pretty much it for my normal standard "must have" list. I carry in the truck. I also always carry a smaller floor jack in the truck. I've never used it camping though, but have a lot around the house. But it's always near me wherever we go. I have one tool box that stays in the bed of the truck. When it gets full of 'stuff', that's enough. No more.
I have in the past attempted to carry socket wrenches, power tools, and a bunch of other stuff, that never got used. I have found that if something happened, or broke, it could wait till I got home. We've learned to improvise almost every situation, and always have a back-up plan or idea if something happens.
If something major happens, like a flat tire, I'll just call for a tow truck or help from any where we might be. And that has never happened to us, except once, several years ago, when the front differential in the 4x4 truck we had blew and we had to have the truck towed, or actually flat bed towed, to the nearest Chevy dealer, who repaired it. The camper was not in the "best" spot while the repair was being done, but it was "safe". The cost of the repair was over $2000 and it's quite obvious, even if I had all tools myself I still could have never fixed it on the side of the road!
If anything major happens to the camper, we'll just deal with the issue right there on the spot. If it's something "major", chances are I won't be able to fix it myself anyway, even if I had an entire garage full of tools. If it's something "major" it can wait till we get home, or call a mobile mechanic, or have it towed to a service facility.
More than carrying a bunch of stuff you'll never use, you need to really consider alternative ways to function so you can still continue to enjoy the trip and not be paralyzed because something minor happens.
We always have an old style cooler with us.
If the refrigerator goes out, we'll simply revert to the old ice chest.
If the water heater goes out, which actually happened once last year when I burned it up with no water in it, we have alternative ways of making hot water and I have since found a way to still take a warm shower, and it works very well in in pinch.
If the stove goes out, we have electric skillets and griddles, or a camp fire.
If we have a flat tire, I have a credit card.
Good case in point: We woke up one morning at the campground with no power. The entire campground was out of power, and no information when it would be restored. The wife is a coffee drinker and she wanted her coffee in the morning. Problem? We had only an electric drip coffee maker. Solution? don't get upset, just improvise, think outside the box and use your head: I used a funner for food preparation, put a coffee filter in the funnel, put the ground coffee on top of the filter, and then poured boiling hot water from the gas stove top into the funnel and let it drip into a cup. Yes, it was a slow method, but she got her coffee that morning and she thought I was a genius and I was her hero for the day.
We sometimes bring our bicycles with us. When I do, I'll bring along our small air compressor and an assortment of wrenches or sockets and Allen wrenches that fit all the parts on the bicycles. Usually, these are just a couple extra items that will end up staying in the tool box anyway. If the bicycles are not with us, no need to have them.
When we carry the canoe with us, I have a separate set of "must have" items we bring along, specific for the canoe. If the canoe is home, those items stay home too.
Bottom line ....
Take a good look at the camper, the screws, the bolts the way things are put together. Then find the tool that is needed for that item, and bring those tools only! Unless you are planning on replacing your auto engine on the side of the road, there's no need for a garage full of tools you'll never use, and don't need because they really don't fit anything in the camper! (really!). Simple is better.