Holy cow. Your daughter is getting plenty of fat by eating avocados every day!! Those things have about 40 grams of fat apiece!!
Sounds like you have a vegetarian on your hands :) A raw, whole-foods one, at that. Trust me. She's way better off with the avocado than the spaghetti and meatballs or the chicken and cooked veggies. Serious. But try this: think of her snack times as small meals. She won't think of them as food-fight territory so much as dinner time. Make sure that her snacks are all very nutrient-dense and get that variety in there (since babies cannot live on avocados alone).
Don't be a short-order cook, that's for sure. But just ask her what she wants, and give it to her. I read about a study that shows that toddlers eat what their bodies need.
In fact, try the "nibble tray" - use an ice cube tray and fill it up with all variety of choke-proof foods. I mean, really get your creative juices going. Hummus. Blended kidney beans and honey as a "dipping sauce" for whole-wheat crackers (or whatever else she wants to stick in there). PB, sure, and mango and soy yogurt and cooked Swiss chard and sweet potato. Quinoa, brown rice, really, anything that's super healthy. Then, she can eat whatever she wants. And you get the rest for your own snacks :)
Then, if she doesn't eat her dinner, at least she's been getting her nutrients through her snacks. Think of dinner as just another snack. No law requires that they get their nutrients in at meals. In fact, snacks in general should be super healthy, anyway. Those growing brains and bodies need all the goodness they can get!
As for going to bed without dinner: no child will starve in the face of food. If she misses a meal or two, it won't hurt her. Many kids just don't want to eat some days of the week. They make up for it the next day or two. Very very common and fine. Her refusing some meals might be her way of saying she just doesn't want to eat then, period, unless it's a treat like avocado (ever feel full but still want that candy bar? ;)
If she comes to you later wanting to eat something, give her something healthy.
L.