I, too, have two generators, a small, light, quiet 1800 watt inverter generator primarily for camping, and a big, heavy, noisy 5500 watt standard generator for the house and the annual outage caused by storms, and paid for by the frozen food we didn't have to throw away after the last such event.
The little one will power everything in my camper except the AC, which the big one would handle with ease. But the big one isn't going camping with us because frankly, I have no way to get it to camp. It is too heavy to put in the back of my TV, and other campers would riot at the racket.
If you want to have just one, and use it for both, it is going to cost you big bucks, because it will have to be both light and quiet as well as powerful, and now you are looking at the sort of contradiction that always costs lots of money, and generally leaves you with delicate and temperamental machines, that cost much more to run and maintain. My two cost me less than $900 together. The closest I could get for a single unit was over $2,000. The $1100 savings will pay for a lot of camping trips.