Here's one more vote for, find an auto parts store with a large parking lot, and do it there. You can buy the oil and filter there, and dispose of the old oil right there when you're done, making it pretty convenient. Just make sure you bring plenty of rags or whatever for cleaning up any accidental spills you have.
That, or just do it there at the campground, quietly and discreetly, and don't make a mess. Odds are as long as you don't make a mess (or clean up real good what mess you do make), and be somewhat discreet about it, nobody won't say nothing.
With RVs, doing the oil change yourself is a no-brainer since it can save you a lot of $$. Most shops that are willing to work on RVs and do this for you will charge you an obscene amount of $$. I probably save a good $100 or more every oil change by doing it myself.
Will and Cheryl
2021 Newmar Baystar 3014 on F53 (7.3 V8) Chassis ("Brook")
2018 Jeep Wrangler JK ("Wilbur")