Caroline skipped the better part of childhood.
You have the meaning of skipped, and this might just be a Brit English thing but "the better part of" often means "the largest part of"
the better part of
Almost all of; most of.
‘it is the better part of a mile’
So this means that Caroline missed most of her childhood.
I just did a quick search and found this book
Caroline skipped the better part of childhood, never cared about
sneaking off to go swimming when she was supposed to be hanging out
the laundry. She never begged for seconds of Grandma’s banana pudding
or lied about brushing teeth. It would seem, however, that the chance
to see her future husband is the one thing to give Caroline some
gumption because before Annie can grab hold of Caroline’s arm or
sweater or any part of her, Caroline has pressed her palms on top of
the fence, jumped, plopped her hind end on the flat rocks, lifted her
legs, and dropped down on the other side.
If this is the text you mean, Caroline was always rather grown up, she didn't do the other childish things other children did, she went straight from baby to boring sensible adult, apart from 1 small item, seeing this boy or man.