My daughter is also 3. It seems like the more I battle, the less she eats. I definitely make no threats except to say in a pleasant voice, "I hope you will enjoy this. It's one of my favorites." When she doesn't eat I remind her that there isn't anything else before bed. I also try to include one thing she loves when I'm trying new things. (usually strawberries or cut up bananas) I also am not playing short order cook. I think you hit it on the head when you said "this new phase". She needs to assert herself as an individual and this is a classic way to do it. My husband is the master at making eating her idea. She always eats more for him than for me. ;+(
Good luck and never let her see you sweat!