Definitely keep trying.... the new flavors and consistencies might take some getting used to but if you are persistent and creative I think she will come around. Mashed potatoes are a great dish to sneak other vegetables (cauliflower, spinach, onions, broccoli, etc.) in or even add something like the peas. From there you might be able to try sweet potatoes or even a baked potato with vegetables and cheese. I like to make smoothies and frozen popsicles using 100% fruit juices or the fruit and vegetable juice blends, you can also add yogurt to them. You could also make your own fruit and vegetable juices if you have a juicer and the time :) We try to eat most meals at the table all together so our daughter sees that we are eating healthy fruits and vegetables too. Rice is another dish that has a somewhat mushy consistency and mixes well with lots of vegetables. I would keep trying new things but not forcing anything on her. It sounds like you just have a strong minded little girl who knows what she wants! :) Good luck!!
And another thought... fresh veggies or fruits with a little dip (like yogurt, ranch, hummus, and even peanut-butter when you introduce it) might be fun for her because she can feed herself and use "big girl dips" too.