Wow! Your options have been significantly narrowed. The only thoughts I have: vegan chili; rice pilaf (w/out nuts, of course); vegetarian spring rolls (use tapioca flour wrappers); lots of different soups (vegetable broth based); some winter squash based items (like a nice butternut squash risotto, perhaps using a mushroom based broth and without cheese); perhaps a "meat" dish with substantial mushrooms substituted for the meat. Alternately, you might go with take-out from a local vegan restaurant (actually, not kidding - this combo is really hard). Or you can go tough-love and have one or two items that fully meet the above, and then only further accommodate those with true allergies/sensitivities (the picky kids get the choice to eat what you are offering or not; same for vegans/vegetarians -- however, taking care that nothing you offer includes "dairy, egg, sesame, lentil or nuts"). You can't be everything to everybody all the time; just isn't possible.
A glass of water. Or a restaurant. :-)
I wouldn't even try. Tell them to cook for you.
You could do tacos on corn tortillas with a variety of fillings for people to choose from. I had a vegan one this weekend that had tofu and kimchee, I've also had one with roasted eggplant or just black beans with radishes and pico. Here's a recipe of my own that I use for 4+ kids. It has meat but you could serve that separately for the meat eaters and offer some avocado and grilled tofu for the vegans. I've also served it with rice noodles as well. http://food52.com/recipes.... Quinoa pasta with a butternut squash sauce (or regular tomato) and a salad. Maybe offer some meat balls on the side. Good luck!
1) POT STUCK BRUSSELS SPROUTS http://food52.com/blog... with polenta
2) Guacamole Quinoa: http://food52.com/recipes...
3) Curry! http://food52.com/blog...
4) Veggie Burgers http://food52.com/blog... + gluten free buns, and maybe some sweet potato fries
4) Soba Noodles http://food52.com/blog... (make sure the variety of soba noodle you get it is gluten free, sub sesame/nut oils for vegetable oil) + fried tofu
When all else fails, make a giant pot of gluten free pasta with a ton of vegetables and beans
Bean chili: vegan, vegetarian, lentil-free, sesame and nut free, no gluten, and loved by kids: http://food52.com/recipes...
I'd make a bunch of great vegetable sides. I'm a vegetarian and personally prefer eating a bunch of sides as opposed to centering a meal around a main. I wish more people would think of meals this way. One of the two current contest finalists could be great. You could also do a sweet potato mash or something with squash. Sauteed cabbage. Quinoa is another great option. There are some great recipes on this site for all of the above. Don't think of yousf as being limited. There's a world of great produce out there waiting to take center stage.