There is a
POV chapter from the father in the webnovel for when he finds out the MC left.
From what I got :
He was not satisfied with the wife's treatment, but left it alone as the MC was not complaining, and I think he was to busy with work.
But the bigger thing was that he felt the MC should have been allowed to go to the school, and it seemed like he felt little sis would not pass the entrance exams since she is not a good student, so the mother's "justification" was pointless anyway.
I get the feeling he might have put his foot down and said the MC gets to go to school had she waited a few hours before running away.
Also, I was scanning the manga Raws, and it looks like he slaps his wife when he finds out what happened (side chapter right after ch 2)