I dont have a 3 year old to contend with, but ive had my moments with my little girl! Some times have been hard - like you no matter what i gave her she wouldnt eat it and it got thrown on the floor which is so frustrating.
I dont want to speak too soon but things are going really well now. I dont make a big deal out of meal times, if she doesnt want to eat then she doesnt eat - but she knows that theres nothing else. I know it can be really hard when you know they havent eaten it, but if they know that theres something better on offer then they will try for it! I didnt get stressed when isabelle refused to eat either - i think they pick up on that, and i think a 3 year old would especially and i think she would play on that, they are very clever little things!
I think you just need to be persistent. If she refuses to eat then say that there is nothing else - and follow through with it! i know its hard, but she will soon learn!
hope i havent sounded patronising in this post, although i only have isabelle i have a ton of nieces and nephews that ive had this experience with!
either way, i hope you get things sorted out quickly!