What makes you think that by forcing her to eat healthy food that you are creating a negative relationship with it? If anything, you are teaching her how to eat. If anything she will come to like more foods because she is being made to try them repeatedly. Sometimes it takes many many tries before they develop a taste for a food. I just don't understand because it shouldn't be hard to force healthy food at all. That is our jobs as parents. I hated peas and green beans when I was little but my mom still made me eat it because it was good for me. As an adult, I still don't like them but I eat them because I now realize for myself that they are good for me.
You can't give in to her and not make her eat at least a bit and you can't not make her eat healthy foods. I don't agree with the "they will eat when they are hungry" as you have seen with your daughter going 4 days without eating.
My children have gone through similar things too. I can't tell you how many times my oldest has gone from liking spaghetti to not liking it to liking it to not liking it to now we are back to liking it. Whew! :) Every meal my children have to eat a little of everything on their plate. My pediatrician once said his rule of thumb is they have to eat a bit for every year so if you have green beans and she says she doesn't want them, she has to eat 3 of them because she's 3.
By continuing to reintroduce foods, she may eventually start to like more things again. Sure it won't work for everything but you are her mom and she is going to get very sick or worse if you do not make her eat. I'm not saying sit on her and force it down her throat. Make it fun. If she really doesn't like vegetables, make the other foods on her plate things she likes so only one item is a battle vs. the whole dinner. Hide some ground beef or turkey in some noodles and sauce. I can't tell you how many times my children have eaten onions and green peppers and not known it.
Another thing I would suggest is getting some protein powder. I am about to start doing this with some that I got from Arbonne and mix it in her foods. You can put the vanilla in her milk or the chocolate in brownie mix. Have her help you make dinner. Give her a couple of things for each (veggie, meat, etc.) that she can choose between and make a big deal about her making dinner. You can make her a chef hat by taking some poster board, making a thick "strip" that will fit around her head and staple it closed. Then from the inside put tissue paper that you have overlapped almost like they do those tissues when you are getting a perm. Staple it to the inside and then fluff out the top so it looks like a chef's hat.
When you think of the alternatives...her getting sick especially something that could cause severe damage if not worse...I think it's time to pull out all the stops. We play as a family every night before the boys go to bed. We can't do that if they don't eat what they are supposed to and it gets too close to bedtime or maybe they can't have dessert. Now is the time to teach your daughter that you are the boss and what it means to eat healthy. Like I said, we've been there a few times but it just isn't that much of a fight because we don't let it. Our boys know they have to eat because we love them and want them to grow healthy and strong. They even recite it back to us they've heard it so much.
I wish you the best. I really do and feel for you having a strong willed child but whether she knows it or not, YOU know she has to eat and you must find ways to get her to.
I hope you keep us posted.