As a motor homer myself I would say the most popular portable grill that I see in our travels is the Weber Q series. Easily can cook for the number of people you are talking about. It can utilize the small portable 1lbs cylinders or you can opt to utilize a 5 gal cylinder,
If you can find a Holland Companion (Company just closed) would highly recommend that. Simple to use, it’s a propane mizer, darn near impossible to burn anything.
For charcoal any of the portable Weber’s like the Smokey or Jumbo Joe, you might want to look at the PK grill also, They have some innovative stand options. Built like a tank will never rust and it will out last you.
I have been in some campgrounds that get finicky about charcoal grills with some crazy water hose requirements but don’t bat an eyelash at a gasser.
Not an RV'er so maybe Tiewunon could input on this. However, the few I know say that some grounds do not allow charcoal because of ash. Again, not sure how true, just what I've been told.
That being said, I agree with the Weber Q series. But I like the brand so that could be it too. Another option, and one I have enjoyed a lot for things like breakfast is a flat top. Blackstone has a 17" table top griddle. It will work off of the small gas cylinders. Both together and you could cook just about anything you can think of.