I don't think it's very common for there to be gluten in laundry detergent. Shampoo and soaps are another matter - I bring my own.
I look for hotels with kitchens, or vacation condos. I am not comfortable eating out very much unless it's at a dedicated gluten-free restaurant.
I bring a roll of tin foil and line any baking sheets or whatnot before using. The first thing I do when I arrive is re-wash all the dishes and utensils. I don't use the toaster at all. If there are plastic or wooden utensils, I don't use those either.