Obviously her parents aren't firm with her at mealtimes to eat healthy food and give in to her which is not a great parenting choice. However, you must stick to your meal plans and keep providing her with the healthy choices but just give her a tiny bit of everything. If she's hungry and she learns there is no other option she will eat eventually and give up the power struggle. She knows she controls things at home but she will learn that she can't control things at daycare.