She's over-tired.
My son is like that.
He NEEDS to nap. Even if he gets a good night's sleep.
My son gets rougher/more hyper/and more impatient, when he is tired.
Going to school, TIRES out a kid.
They have nil patience, when tired.
Hence they act out.
My son is 5. He's been in Kindergarten for 1.5 months already. I have him nap after school, when need be. I KNOW when he needs it.
Also have dinner for your daughter, EARLIER. Many kids, like mine, cannot eat when tired, even if they are hungry.
Make everything - dinner, bath, getting ready for bed- earlier.
Going to school for a young child, is very tiring. They are at school, on task all day. When they come home, they DEFLATE. And are over-tired. You need to let her.... deflate and UN-wind, after school.
Have QUIET time at home, after school. They need this. They were ACTIVE ALL DAY, at school... and overly stimulated. Hence, they NEED to just relax at home. They are already spent.
When a kid is over-tired... they cry more, get more fussy and tantrum. This is a CUE, that they are overly... spent.