I carry a tool box in the back of my pick-up truck that stays in there all the time, camping or not. It contains some basic hand tools, pliers, flat and Philips screw driver, knife, extra parts for my Equal-I-zer hitch, tape, stuff like that. It's stuff I use around the house too. It's basically my emergency break-down kit for any reason.
Specific for the camper, I have one of those square sided screw drivers that fits those square headed screws all over the camper. Of course, the stabilizer jack handle, a small carpenter's level, a ratchet and socket that specifically fits my water heater anode-rod drain plug head (it stays with the camper all the time and never leaves). My tool box also contains my blow-out plug to use with my air compressor. I keep it in my breakdown box so it won't get misplaced, although I use it only 1 time a year.
I carry a hatchet, which doubles as a hammer, bungie cords and rope in my truck shell tool boxes (always), ratchet straps (several of them)... for the canoe and other uses.
I do bring along an electric drill and the bit that is to be used to retract or extend the slides and the awning in the event of a failure, they can be open-closed manually. But the actual drill goes from the truck to the house all the time. The bit stays in the camper permanently.
When selecting tools, it's not so important you have a "bunch" of stuff, it's more important you have the "right" stuff. If you have a unique item in your camper that requires a special tool, then by all means, carry that tool. You may never need it, but that one time you leave it home, you'll need it.
Of course, what you carry with you is also determined by how far from home you are traveling, if you are full timing (and have no S&B home to return to), or if your in a location where you have relatives or friends that can help you in a pinch. This also drives what kind of tools you need.
80% of our camping is right in Indiana. If something happened, pretty much anywhere in the state, it would not take more than 3 hours any direction to get home, get the part or tool I need, and return back in another 3 hours. However, when going to Florida over Christmas, I take along a few extra precautionary tool. For me it works.
There again, take the "right" tools, not necessarily just "any" tool so you have something.
Really, look at every item in your camper and ask, what do you need to take that apart. Then create your tool list from that.