You don't mention whether the child has behavioral problems or not.
If she exhibits them, the following story may interest you:
I once knew a child who used to be hyper, obstructive, obnoxious and disruptive at social gatherings; This child ate a lot of sweets/cookies/macaroni/cake (White flour) and those were the things she loved and wanted.
One day she was acting very strongly according to her usual pattern- cranky, loud and temperamental- had been eating cookies/junk/ice cream all day, and I handed her protein instead. Since she was hungry she ate it, and within less than a minute was nodding off..
I pointed this out to her parent and said, "Look,did you see what just happened? She ate protein instead of sugar/white flour and now is immediately sleepy. That means her blood Sugar is the problem, and that is causing her to act this way. Protein is what she needs, not this other junk."
That parent listened, and the child is very different today.
Maybe you need to make that test with your daughter, and then show your wife the difference..