Oh my goodness, I'd be concerned too! That's a whole lot of drugs for a 3 year old. :-(
Your daughter is so very lucky to have a parent who is looking beyond conventional wisdom already. Have you read Mary Sheedy Kurcinka's book (edited to correct title) Raising Your Spirited Child? Seriously, go buy it today if you haven't read it already. I think you'll find it tremendously useful, though its focus isn't dietary intervention.
I definitely believe a child's diet can influence behavior. If the food she's eating is making her feel bad, of course it is going to influence how she interacts with the world around her.
A PB-type diet, with higher protein (edit: hers sounds inadequate: no meat?), high fat, and very low sugar/starch might make a big difference, but given what you've written, it might take more than that.
Some parents notice HUGE improvements in behavioral issues, including attention/hyperactivity disorders, after gluten and dairy are removed from a child's diet. You often see this referred to as a GF/CF (gluten-free/casein-free) diet.
The Feingold diet is another one to consider for behavioral issues.
But you're right, the more difficult issue will probably be convincing your spouse to give it a try. Read up on dietary interventions, and poke around some online forums for parents who are successfully using dietary interventions for attention/hyperactivity disorders. (Google to find appropriate forums.)
Then offer to clean out the pantry of whatever foods you're planning to eliminate, and offer to personally take over the grocery shopping and cooking. Keep notes on behavior during the elimination, but don't draw any conclusions yet. After a strict 2-4 week elimination of a specific food, like dairy or gluten, try adding it back as a challenge. Feed a whole bunch of it in one day, and then make more observations over the next few days. If it doesn't seem to make a difference, add it back. If it does, take it out again.