your daughter's hair seems very healthy. healthy hair in her texture shrinks. that's just what it does because shrinkage is as much a property of our natural hair as our curls, coils, waves, frizz, and fuzz are.
i'm more concerned about the child calling your daughter names. i'd definitely bring that incident to the director's attention. your daughter has a right to feel comfortable and secure while in daycare and not be the target of demeaning remarks by other kids. that behavior needs to be nipped in the bud.
unless you keep her hair suffocated with heavy, coating products that weigh down texture and counter shrinkage, you should enjoy, and teach her to enjoy, her hair texture instead of trying to fix it.
personally, i'd change to more natural and milder products for her hair and forgo the use of petro-based products. i wouldn't obsess over fighting the shrinkage, but focus on retaining hair growth by keeping the ends healthy and by not using tight hair styles and accessories that can compromise the health of her scalp and hair.
i'm also concerned that at the tender age of 4 she's already showing that other's opinions of her is shaping how she feels about herself.