Please tell me that my daughter will not be eating chicken nuggets for the rest of her life

My daughter is 5 and is a picky eater at home. She goes to a home-run daycare/preschool and eats the lunches prepared by the staff -- they've always said that she's a good eater. But at home, all she wants is chicken nuggets and a vegetable (carrots, cucumber, broccoli, or green beans). We've been trying to introduce her to "big girl food" (what me and my husband are eating), and I thought we'd made a little progress. But then we had roast chicken the other night and I put a few pieces on her plate.

She flipped out. Crying, screaming, the works. She grabbed the plate and threw it on the floor. I lost my temper and yelled. I feel really bad about that. I wish I hadn't yelled. But the pickiness is driving me insane. I know it won't last forever, but I just wish we could get beyond it.