OP: I think this is a great question. It's one that we had also before we started full-timing. Our 9-year-old son is basically allergic to life.
His allergens are:
Trees, Grass, Weeds, Mold, Dust, Cats, Dogs, Peanuts, and Tree Nuts
He has allergy-induced asthma. Carries epi-pens at all times.
He takes 2 tsp of Allegra in the morning and 2 tsp of Zrytec at night.
Our sticks and bricks home is in Ohio, and the winter-time was the only time he could go off his meds due to the freezing weather. We have his mattress and pillow encased in special covers. He takes a shower every day to get rid of pollens. I try and not clean with him in the same room. We don't have pets. We don't smoke.
Traveling and living in an RV worried me mostly because of constantly having to relearn which foods are safe for him. Going to a new grocery store takes more time anyway, but then having to read the ingredient list on each and every food is time consuming (BUT not negotiable). Dining out at restaurants requires phone calls to the managers in advance, checking restaurant website, speaking in person to managers, etc. There's no such thing as spontaneity.
BUT...we do it all. We don't want him to allow his allergies to stop him from doing what he wants to do. We just makes things as safe as we possibly can for him.
Roadhouse 4 Us