S.,
I was diagnosed last year with gluten intolerance and had to go grain-free. My nearly 3-year-old was symptomatic with me. While I haven't had to drop milk, I can relate to the major lifestyle change. I'm expecting a boy in June; my doctor says there's an extremely high chance that he'll have the same genetic tendency.
Our family found it easiest (and my wonderful husband was willing) to just eat my diet. The first week or two is the roughest as you try to figure out what you CAN eat. Be prepared for the first month or so to spend hours planning meals (and not going out). But then it really DOES get easier (and you do save money not going out as much).
My suggestion is to start with whatever dishes are your family's favorites and find ways to adapt them. For example, we love tacos--which we now eat in lettuce instead of tortillas. For stirfrys, we use cabbage leaves (instead of rice as a side). I thicken with either arrowroot or potato flakes instead of flour or cornstarch. As you just keep trying and working, things really do get easier. I've now built up a binder of recipes (that I've annotated) so I can remember how to make them--or my husband can.
Where you both work, it's probably hard to find time to cook. (But the reality is, this kind of diet does not lend itself well to boxed, canned, fast food--so you end up needing ot cook.) But you can cut corners: use frozen veggies whenever you can, cook once for 2-3 nights, use prepackaged fresh veggies, etc.
My nutritionist has his wheat patients go grain-free; in my case, that was the only diet that brought us relief. The gluten molecule has two portions: gliadin and I believe glutein (which is the one science has studied and is only in wheat and rye); the other portion (gliadin) is in ALL grains. One possibility is to try traditional gluten-free stuff for a while, and try a grain-free diet for a while (I noticed a difference in just 2 days).
Most traditional gluten-free flours, etc., are rice- and corn-based. I found that the lack of fiber resulted in sugar rushes. With your daughter's corn allergy, you'll have to take care in trying any of those.
I tried some of the "gluten-free" products for a while; they were expensive, and rather refined. I've had better experience, better quality of meal, and saved money by just cooking myself.
Whatever you decide, breakfast is the hardest. I usually do salmon cakes (use potato flakes instead of crackers). You could try egg replacers, too. Another possibility is homemade pan sausage (made with ground turkey or whatever meat you want); I just add spices. I've found some good grain-free pancake/waffle recipes that, if you could find a substitute for the egg, would work for you. One is based with almond flour (from the book Grain-Free Gourmet or its sequel); the other is based with coconut flour and uses coconut milk (several on the web; there's also a Cooking with Coconut book). Another possibility is to do breakfast smoothies--you can put nearly any fruit in. Since you can't use milk or soy, try the pear juice from canned fruit or a small amount of juice or coconut milk to give it some liquid or froth. My way of making it through breakfast the first month or two was to find the nicest fruit I could, and eat that with breakfast.
I would heartily recommend the Grain-Free Gourmet book and its sequel to you (available on Amazon). They mainly use almond flour, but everything is grain- and dairy- and refined sugar-free. It's the Specific Carbohydrate Diet. It's a bit more restrictive than my diet, but hey, it gave me pancakes, crackers, and bread again. The almond flour is expensive and is not calorie-free, so we use it mainly for treats (pancakes on weekends, birthday cakes, etc.). It's fabulous for cakes and cupcakes--my husband couldn't tell the cupcakes were "different."
I'm just now looking into coconut flour instead of or in addition to almond flour; it's half the price, and lasts a lot longer (because you use less of it), and it stores for up to a year at room temp. There is also a recipe out there for pasta made with yam flour (available in the African / Carribean section of supermarkets).
The Grain-Free Gourmet approach (specific carbohydrate diet) is bean-free, which I don't have to be. Beans can open up a whole new world for you all, if you're not used to them. They are a great carb, with lots of fiber. I was never really big on sandwiches for lunch (too many as a kid), so we often eat a bean dish with meat and veggies for lunch. Some are Mexican, but a lot aren't. I have some I really like, or you can google "grain free bean recipes," or look at adapting some from cookbooks. You can either buy canned for convenience (be sure to read the label), or make your own. To save time, I do a couple batches at once, and use a pressure cooker then freeze whatever I don't need to use right away.
We switched just a few months after my daughter's 2nd birthday. So she still remembers (and asks for) pasta, bread, etc., which is hard. My explanation is it "makes our tummy hurt." About 6 months ago, I also had to drop all refined sugar for men (long story), so that has made it even more difficult for me.
We eat what we're supposed to at home, and don't keep anything that she or I can't have in the house. At friends' house or playgroup she sometimes gets things she shouldn't; I just try to minimize the quantities (in our case the reaction is just gastrointestinal inconvenience, not life-threatening). The magazine "living without" and their website has some nice resources for parents trying to navigate this kind of situation with kids who have allergies or intolerances. I've learned when we go on outings to take our own snacks (100% juice packs, fruit strips, nuts, dried fruit) since most food sold in concessions or restaurants or vending machines is problematic. I also keep some in the car for times when errands, etc., take longer than usual. (Not all convenience / drugstores have stuff we can eat--and I don't usually want to pay their prices anyway.)
Sorry if this was way too long, but my heart goes out to you. I've been there, even if the details are slightly different. It's so hard emotionally to see what they're missing out on, and you don't want to be a food Nazi and yet you need to protect them from what would make them sick.
Feel free to email me if you have any questions or want any more information.
C.