Haven't painted a travel trailer, but
have painted walls and cabinets in manufactured homes. Since the wall coverings and most of the "wood work" are vinyl or vinyl-covered, the secret to getting good paint adhesion (sp) and coverage is the prep work. I'd start by washing every surface with a solution of TSP - Tri-Sodium Phosphate. You can get it at HD or Lowes, and make sure you wear heavy rubber glovers. Next, rinse everything AT LEAST TWICE to remove the "grit" left by the TSP. Then, paint everything with a good primer. I recommend "KILZ". I know, all the modern paints say the have primer in them, but KILZ will give you better surface sealing over stains and grease (because of its high varnish content), better paint coverage, and better adhesion. Next, you can wallpaper or paint. If you paint, use the highest quality paint you can afford. You'll get mush better coverage, adhesion, and durability. Before painting cabinets, remove the doors & hardware and paint them separately.
Finally, allow the paint to
cure for at least 2 weeks before taking it camping. High-quality paints have a lot of vinyl in them. It's very durable once it's cured, but before that, you can scratch it easily with a fingernail . . . and it will peal like a bad sunburn.
Hope this helps. Happy "modding" and HAPPY CAMPING!