I know in some places, pizza places (like Los Angeles) even deliver gluten/dairy-free pizzas that are delicious. My daughter bakes gluten-dairy-soy-egg free cupcakes from scratch,but Udi's also makes them, and that is sold in many grocery stores. They have fresh and in the freezer section.
Look to Udi's for breads and bread products, but watch out for nuts in some of their products. Ian's has allergen-free Vegan products such as chicken nuggets and fish sticks.
Some hotdogs actually have dairy/casein/whey so be careful.
You can use corn tortillas instead of bread.
We make our "sandwiches" with no bread. We make wraps using luncheon/deli meats, with lettuce wraps, and put inside things like tomato or celery, pickles, avocado or whatever we feel like. But there are also gluten-free wraps you can buy.
Other ideas are to make hummus (much cheaper than buying it) and use corn chips (check ingredients), green beans, celery, or carrots as finger food to eat the hummus with. And/or have Salsa dips.
Instead of hotdogs, you can use chicken legs, but even those need to be checked. If it says it has "broth" it may actually contain gluten!! I was shocked that they didn't have to list it on the chicken that they were adding gluten to it!!!