It shouldn't be a problem from a functionality standpoint. Assuming some outdoor separation between the cabin and the motorhome, there generally shouldn't be much difficulty with CO, either; it dissipates outdoors fairly readily due to normal air movement. I'm not suggesting that you skip the alarm, of course.
There may be some code issues with regard to neutral bonding, depending on how the cabin is wired. In this case it should have the neutral and ground separate, and they should be bonded at the RV generator. From your description, I suspect it's very simple—just a wire between the outside plug and a couple of outlets, essentially a glorified extension cord. It would not be a bad idea to see that the ground wire is connected to a proper grounding rod at the cabin.
If the inlet for the cabin is a single 15A plug (a normal household plug), 12/2 would be plenty for a cord unless it's quite long. If it's a 30A plug, 10/2 would be OK for moderate distances. You don't need a three conductor cable unless for some reason you have a 240V split phase inlet, which seems highly doubtful for a single small air conditioner, and is at any rate not the output of any generator that would be in a small motorhome. (The ground conductor is not counted in the wire count of cables).
If it were me, I would probably think about a semi-permanent generator install at the cabin in a dedicated generator shed. I'd think it might be nice at times to not be tied to the RV when you're using the cabin. You might also find that air conditioning is not a continuous requirement, and that running the generator for a half hour or hour a couple of times during the day is sufficient.
Many class B RVs don't have a generator built in...obviously something to check when you're shopping for one.
