Can you try introducing some veggies at lunch time? Salad veggies are possibly less "threatening" than cooked dinner veg.
My ds loves slices of cucumber, wedges of tomato, pieces of pepper, a spoonful of sweetcorn, etc. He even loves olives, which I thought would be too much for a 3 year old. He does eat VERRRRY slowly though.
With your DD being that much older, you have probably got into a set pattern of eating, and she has become comfortable only with what she likes the most.
I think you need to be strong and start serving up more balanced meals. Don't offer any snacks between meals for a little while and see how you get on. Don't pressurise or get angry, just serve it up and leave her to it. A bit of encouragement may help. Or get her to help you prepare the food. Or make funny faces out of mashed potato by adding a few peas or carrots or something.
A balanced meal should be half a plate of vegetables, then for the other half a plate, two thirds of it should be carbs (pasta, rice, potatoes, cous cous, etc), and the final third of that half should be protein (meat, fish, cheese, tofu, etc).
I think you are the key to this, and at the moment she can really only eat what you serve up. If you let this continue, when she's older she'll be going to the chip shop after school and refusing your meals completely. If you can get her into good eating habits now, then I think you can avoid that later.
(Sorry if my views upset - I am a bit fanatical about this though - dh calls me the food police!)