I am also a breastfeeding vegetarian, and due to DD's intolerances we are currently off of dairy, gluten, soy, citrus, and chocolate, and we don't eat much in the way of egg either, so I feel your pain. It's tough, isn't it?
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The way I understand it, it is important to cut all suspect foods completely from your diet, at least until you have your DD at baseline (no reactions to anything you're currently eating, no rashes, etc.), and probably continuing after that, although once she's at baseline you might be able to try reintroducing small amounts of foods that you aren't 100% sure are a problem. For foods that definitely are a problem, I believe you need to have her at baseline for at least six months to allow her gut to heal before trying to reintroduce those.
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I don't know if you need to get wheat completely out of the house (we haven't, since DH still eats it and we have houseguests sometimes who eat it), but I wouldn't let your older DC walk around the house eating things your DD can't have. It would probably be best to either only let him eat that stuff in an area she can't get to, or only have him snack on things that she can also have. Otherwise, the possibility of her getting a hold of some is just too great.
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In terms of staying healthy on such a restricted vegetarian diet, for myself I'm not too worried about it, since I still eat a wide variety of fruits, vegetables, whole grains, proteins, and fats. I wonder if in some ways I'm actually healthier than I was before, since I did tend to rely on those cheap, widely available staples, and I may be better off replacing wheat/soy/etc with a broader variety of foods and thus a broader variety of nutrients. You said your belly wasn't happy about the increased amounts of beans and peanut butter. What about finding more varied sources of protein and fat? You could try different kinds of nuts and nut butters, coconut products, and different kinds of whole grains. Quinoa, for example, is a great source of high-quality protein, and you could have that topped with a coconut milk curry with some nice winter vegetables and a few beans in it. 
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As for your DP, my DH also doesn't feel the need to eliminate gluten and soy from his diet, but that doesn't mean I cook multiple meals. You didn't say whether you or DP are the primary cook or if you take turns, but when you're cooking I don't know that I'd feel the need to make multiple meals. I cook meals that DD and I can eat, of course choosing things I know DH likes, and then he can choose to eat it or not. He mostly eats the things we can't eat when he's out of the house or we're not around, so he's responsible for acquiring/preparing those foods for himself. I just wouldn't want you to make the whole thing harder on yourself than it has to be, you know?
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Also, you didn't say whether you were consuming dairy or not. If you are, and your DD is still getting rashes after you've eliminated all the other foods you suspect, I'd consider eliminating dairy too, since dairy and soy are often cross-reactive.