My daughter is allergic to eggs, milk and peanuts. So, her options are more limited than your sons will be.
Pizza Port has an allergy pizza with Daiya cheese on it. It's really good. Even with the gluten-free crust they insist on using, it's good. (Much better than the Daiya frozen pizzas). I hear that Boardwalk Pizza has the same, but haven't tried it. We have not been offered dairy-free cheese anywhere else and have never been offered dairy-free margarine.
The kids menus aren't great, at least not for my daughter. So, we often share a meal. You're going to find safe fries just about everywhere. Adult hamburgers (with bun) are safe at every place we've tried. The hot dogs at Refreshment Corner are safe (with bun). Rancho Del Zocalo has clueless CMs, but if you're persistent, you can find someone who knows what they are doing and can provide a milk-free meal.
We did the Minnie and Friends breakfast at Plaza Inn a year or so ago. They did make her special waffles, which weren't cooked all the way through. After hunting someone down and requesting done waffles, we waited a long time for another set of undercooked waffles. Considering that was the only thing my two-year-old wanted to eat, I gave her a couple of bites of the edges and she ate a few grapes. Not much of a meal. They didn't offer soymilk or margarine or anything. It was a subpar experience for us, except for the characters (which were great).
I haven't checked the online menus lately, we haven't been since February. The last I looked, I didn't see the allergy menus. I did notice that Cocina Cucamonga now has their allergy menu in the app, so that was a good change. I'll have to look online and see what they have listed now.
You're going to be sorely disappointed in the ice cream realm. There isn't any. There is Dole Whip and the new lemon soft serve (assuming it isn't cross-contaminated. I haven't heard any reports from allergy folks on it since it opened) at the Adorable Snowman. Ghiradelli has sorbet, but won't do an allergy order, so it is useless. Clarabelle's in DCA usually has sorbet and will do an allergy order. My daughter had breathing difficulties after eating there in January. So, I'm hesitant to recommend it anymore or take her back there again (though she had eaten it safely previously). Haagan-Daz is closing, so it is not an option anymore either. If you trust Starbucks, they can make a dairy-free vanilla crème Frappucino. My daughter had them safely a few times (at DLR), but then one of our friends had a reaction from one (also at DLR). So, we have avoided them since.
