Disneyland is the easiest place to eat gluten free! I live in Southern California and had an annual pass for years, until that became too expensive. I haven't been in the last year, but I doubt anything's changed. There aren't gluten free options at every location, and sometimes they move stuff around, but it's easy to find. The lists at City Hall have always been at least a few months out of date when I've been there, so be sure to ask at each restaurant first. Some, but not all, places have dedicated fryers for French fires, so be sure to ask. Even if the front-line employee doesn't know anything (which is rare), the managers are always knowledgeable.
Specific places I usually eat are Tomorrowland Terrace and Redd Rocket's Pizza Port in Tomorrowland, and Rancho del Zocalo in Frontierland. Tomorrowland Terrace has hamburgers with gluten-free buns, Redd Rocket's has gluten-free pizza and pasta. Zocalo is a cafeteria-style place, so just walk up to the counter and tell the employee you have a food allergy/intolerance. They'll get the chef who will prepare your plate him/herself. The cheese enchiladas are good there, although the last time I went, they told me the ingredients in the Carne Asada had been changed and that was no longer gluten-free, which was disappointing.
It's a little pricey, but the Storyteller's Cafe at the Grand Californian Hotel is worth it for at least one meal. They don't have a separate gluten-free menu, but almost anything can be modified. The chef will gladly come out to talk to you if you ask (and sometimes even if you don't). It's a good place for breakfast too - pancakes, waffles, just about anything you want, and there's a buffet for the gluten-eaters. During breakfast there's usually costumed characters roaming around interacting with the customers. Don't bother with Blue Bayou, unless you really, really want to eat there. Yes, most things on the menu can be made gluten-free, but the food really isn't very good, and it's ridiculously expensive. The only reason to eat there is the atmosphere.
Every time I've been there, the popcorn and turkey legs sold at food carts around the park have been gluten-free, but check just to make sure ingredients haven't changed.
All the employees I've interacted with seem to not only understand gluten-free, but also cross-contamination too, except for one hapless emoloyee who was probably new at Redd Rocket's once, who sliced my freshly made gluten-free pizza with a used pizza cutter. Fortunately I saw it and alerted the chef, who made me a whole new pizza. That incident is the only problem I've ever had there though.
They do search your bags before you go in, and officialy they don't allow outside food, although they of course make exceptions for special diets. I only mention it though because I've actually never been questioned about the snacks in my purse, even though I know they've seen them, so I think they're looking more for potentially dangerous things than outside food.
Disneyland is the one place I can spend the day out and actually relax and not have to worry about food once. Good luck and have fun!