I would guess that since it's an rv, it already has a beefier alternator from the factory. You said the alternator is putting out 13 volts? Is that from the guage on the dash, or a meter on the battery while running? You should be around 14.2 volts. If you got 13 volts by testing the battery, the alternator could be on its way out. If your lucky and in a rural area, you might find someone who rebuilds alternators and starters. Save a bunch of money, and it's not some "brand new" Chinese piece of shit
I would take it to a parts store and have them measure your voltage at the battery while running.
You could also run a dual alternator setup, at least keep you from draining your bank while the rv is running.
If it were me, I would try to find an old generator out of a boat or rv. You might get lucky and find a nice used diesel. Or grab a Honda is2000 or something similar. Fuel efficient and quiet little generators, and they'll run for years and years.
You have your own property, or you just out cruising the campsites and what not? Out here where I live, a lot of people have rv's that they live in. They get a small rv power pole, run a breaker box and a few plugs, and that's that. Might be able to find something similar. It's perfect for people like us. Far enough away and spread out enough so people don't bother you. Lots of rough people out here, so it's easier to lay low, than say a suburban neighborhood.
I did a lot of research on solar panels. I'll say they are better than nothing. But if you work the cost out, with initial and replacement costs of batteries/panels, electricity from a plant is just cheaper. Not to mention reliable.
What kind of rv you got? I've been looking at school busses lately to convert to an rv. I do metal fabrication for a living, would be cool to convert one into a camper. Then buy a wrecked bus to cut the back 24' off, and turn that into a portable fab shop trailer. I travel all over the country working, would be awesome to carry my whole life with me
And get some leds!!