Hi there...I'm sorry to hear that you are going through this battle. I have dealt with kids seemingly more stubborn than myself when it has come to eating issues. My little girl was about the same age as yours when this actually became an issue for us, so I can totally sympathize!
For the dinner-time food challenges, this is what we did...We would fix a meal that we would ALL eat, because at the age of 3 1/2, my daughter was ABLE to eat everything we gave her (whether she wanted to or not). If she ate only part of it, or didn't want any of it, we wouldn't give her anything else instead of that. There are one or two times that SHE chose to go to bed without dinner. It is not that we didn't offer her anything, it is that she "didn't like it" and refused to eat it. After a while, she got it figured out. And some nights we would fix something that she liked better and didn't have as much of an issue. It is one of those things that you will have to take a stand on. This was worse of an issue with my oldest son because when he was 2, he didn't want to eat anything other than crackers, cookies, breads, etc., thanks to Grandma who didn't make him sit to eat balanced meals. We decided that we weren't going to keep buying him and fixing him his own "special" foods to eat just because he didn't want to eat what the rest of the family is eating. We are now implementing this into our 2-year old, and he is starting to get it.
One thing I also wanted to mention here...we are NOT "clean your plate" people. Our rule is that the kids have to have a little bit of everything, they have to try it, but they can stop when they are "full". Sometimes, they have come back 15 minutes later to finish their dinner if they decide they are still hungry, but we don't ever make them eat everything on their plates.
This takes time, and it is especially helpful if you sometime take some time to explain to her daughter about eating healthy foods, especially during this time of cold and flu. I've told my kids that eating good foods helps them run faster, play longer, and not have to stay in bed because they don't feel good.
I will tell you this. If you are trying to feed her healthy stuff and not catering to every whim, rest in this bit of knowledge...a child will NOT starve himself or herself. They will eat when they are hungry. There could be other reasons they are not eating like illness or fatigue. It may truly be a medical issue, but a normal and healthy child will not allow themselves to starve. Sometimes we think that a child is undernourished just because they may eat a few bites of something at every meal, or sometimes skip a meal altogether, but they will make up for it at another time. Their stomach is pretty much only the size of their fist, so no, they aren't going to require a lot of food.
I hope some of this helps...there are many reputable child nutrition resources out there, one of them is this one:
http://www.askdrsears.com/html/4/T040100.asp
There is lots of good info here and some you might like, others you may not, but it talks about starting your kids on a healthy lifestyle.
God bless!