Frm what i know newborn love to be carried tightly... i feel it might be the car seat is too big for her so she will feel insecure... you might want to out more cushion or cloth to make the car seat just nice for for like being carried. it might also cos when driving the road are bumpy so will frighten them... i suggest you can make the seat smaller so she'll feel like being carried..
whenever andrea sit in the car seat i will make sure i place my hand on her chest. like whenever go over bumpy road i will hold her even tighter so she wun feel frighten. maybe you can try this.