Looking on the internet deeply has found these results:

the children are home late from school is the most popular phrase on the web.

the children are late home from school 1603 results on the web	the children are home late from school 1283,000,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
It doesn't look like this phrase is very popular! The search could not find any examples on the internet.	I have to pick the children up from school. Two years ago you came home late from the office and you were attacked by two guys. It's probably just Homer coming home late from Moe's. We got home late from a camping trip, so he was here. For when children with Georgian names are expelled from schools, all our children are at risk. Did you come home late from the dance last night? My husband had come home late from the bar. I saw you come home late from the union meetings.

the children are late home from school

1603 results on the web

the children are home late from school

1283,000,000 results on the web

More popular!

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

I have to pick the children up from school.
Two years ago you came home late from the office and you were attacked by two guys.
It's probably just Homer coming home late from Moe's.
We got home late from a camping trip, so he was here.
For when children with Georgian names are expelled from schools, all our children are at risk.
Did you come home late from the dance last night?
My husband had come home late from the bar.
I saw you come home late from the union meetings.