Hi,
One thing I haven't seen mentioned is a lack of sugar in her diet. Yes, fat too, but if she is eating meat she is likely getting fat in her diet, although at two having some kind of milk or milk alternative(not the store bought milks) is going to be of importance and also... fruit. Kids need almost the same quantity of sugar and fat in their diets. Candida overgrowth comes from fat or other things blocking the body from absorbing the sugar in the blood properly. So one piece of fruit a day is going to cause her to want more and more food for sure, and especially if she is not also eating grains which is another form of sugar for the brain/body. The first three years the quantity of glucose to that massively developing brain is so important and while protein is extremely easy to get because it is contained in everything, and while there is at least a little fat in most things, at this age kids need a lot of fat and a lot of natural sugar.
Also, I couldn't tell from reading, but you said you don't eat much around her, I would try to eat meals together with her and eat the same foods she's eating in front of her. That diet really doesn't sound that restrictive for a 2 year old, which is still very young... or even an adult, if you were eating seasonally that quantity/variety would change with the seasons and would actually be a very healthy and pleasurable way to eat, if you really think about it. Anyway, the point is, I think she's getting enough variety and I don't think that is the problem, just that she needs a little more interaction during meals to understand the "food thing" (I always see a little obsession, figuring things out with kids at this age) and that she needs a little more fat and fruit, more than likely.
I would look into a few different(and opposing) ideas on nutrition, allergies, children's health, candida, etc.
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