There are few studies that provide good evidence for the effect of food on dog behaviour. There is, as usual, a lot of misinformation out there. Jane is right to say that it will be very difficult to provide a home-cooked diet that is not only balanced, but also manipulates the ratios of nutrients that might affect your dog's behaviour. It can possibly be done but you would have to do a lot of work to understand the variables. Tryptophan and tyrosine appear to be the usual compounds that are considered to have some effect on behaviour as they have an impact on the levels of certain neurotransmitters, but the studies are usually looking at the effect of these things on aggression. Supplementation with tryptophan is a possibility but over-provision is also a problem and I would not consider that without expert advice.
The likeliest thing is that your dog is just displaying her character or maybe has some mild behavioural issues. I would go with Jane's suggestion of feeding a good quality balanced food and possibly look at stretching her mentally with things like clicker training, as well as physically through exercise.