I am not sure of your kids likes and dislikes, but I can throw out some options that maybe you haven't thought of.
Paradise Garden Grill: veggie and tofu skewers served with rice pilaf and your choice of sauce. There are vegan sauce options, which should meet your dairy free needs.
Lucky Fortune: Asian stir fry, there is a vegan sauce you can have on the stir fry
Boardwalk pizza and pasta: ask about pasta options, but we were made GF pizza crust here. It is worth a shot to ask if it is dairy free as well.
Cucina Cucamonga: Mexican food with corn tortillas, no cheese, no sour cream.
Pacific Wharf Cafe: the Vegetarian Chili was dairy free (vegan) when you asked for no cheese on top (they would sprinkle it on before serving).
Jolly Holiday Bakery: they had a salad here that was veggie and whole grains with a basil dressing, maybe not for the kids, but for you?
Rancho del Zocalo: same deal as Cucina, take off the cheese and sour cream and sub flour tortillas for corn.
Riverbelle Terrace: giant Becky Thatcher fruit plate is really good
Royal Street Verandah: we were told the veggie gumbo was vegan, but do ask and see if still is, served not in a bread bowl, obviously.
Bengal BBQ: skewers with no sauce, again ask here because some reports have the skewers cooked with butter, but others say it is a different oil.
Those are the ones I can think of from the top of my head, hopefully others chime in. We do a lot of table service, since they do seem to be able to offer more choices. I hope some of these work for you.
