Can't speak to the RV-specific stuff since we haven't made our maiden voyage yet (waiting to take possession!), but I have gone on long trips up to 3 months (and 3 continents) with suitcases, rental cars and motels.
My tips would be:
Weather changes over a month. Pack clothes, shoes or supplies for either possible extreme during the time/place. Also one fancy outfit just in case you end up wanting to go somewhere where your normal clothes would be out of place.
Look into how to launder undies etc. in the sink to stretch out your need to visit the laundromat. Or just bring extra of those items. (Though I'm a huge fan of wash & fold, where you drop off and they do the work. Not every place has them.)
I second the prescription stuff. Also OTC stuff you need at least once a month. Even in a motel with a little zippy car, it's annoying to have to make multiple stops to pick up Tums or a refill. Trailer/TV seems like a much bigger annoyance. It's much better to have the basics, like bandaids, Neosporin, allergy meds, Imodium, clippers, ibuprofen, earplugs, sunscreen, bug spray.
Look at the other little conveniences you use. On long trips, I pack a nice Bose travel speaker - it adds a couple pounds but makes everything much nicer. Your AS probably doesn't need it, but that kind of thing that makes a trip feel homey and enhances your enjoyment. Your cozy PJs? Scented candle? Favorite book? Little piece of art? USB charger cables for both the lounge AND bedroom? That.
My traveling companions are always jealous when I pull on my favorite yoga pants and fluffy socks to lounge in and they are stuck only with jeans.
For your home: You'll feel better if you know somebody will check in once a week just to be sure there are no surprise leaks or anything. A trusted person should DEFINITELY have a key, even if they aren't going to check weekly. We leave a list of our usual contractors etc. for our friend just in case. Personally, I leave a signed blank check with my house sitter to be extra prepared. (Granted, our house is old and persnickety.) We also have webcams so we can sneak a peek just to be sure things look fine.
(Note: We've never actually had a problem with the house while traveling, so I don't mean to scare you. But one month while at home we had both a roof and radiator leak. Don't worry, prepare! is my motto.)
USPS hold mail, or get a neighbor to pick it up for you.
The most important accessory for a long trip though... is embracing the nature of long-term travel. It's very different at first! You'll find your routine but it'll probably take a few days.