The OP doesn't clarify the age of the lads using violence towards their mothers. Lots of discussion here about the age at which children can be said to be using domestic violence against parents.
Toddlers often lash out, surprisingly toddlers who have never been in an environment where adults smack our yell, will smack and yell themselves. It's a perfectly normal developmental stage. By 3 or 4 years, tantrums like you see in 18 month olds are largely gone because parents manage them well.
The family Chewbacca uses to illustrate parenting that isn't meeting the needs of the children, definitely need help. Many schools have close links with their social work teams who used to be able to offer 1-1 advice and referrals to sure start/other family centres for parenting skills groups. The mum definitely needs that kind of support and it would also enable a proper assessment of the children's needs. Whether any resources are left after 10 years of austerity, to meet those needs is another story.
Our prisons and youth offending centres are full of boys who were neglected and/or subject to extremes of physical and emotional abuse. The levels of illiteracy are high. Children can't learn when they're terrified or exhausted as too many children are.
There is a lot of focus on the 'old methods, clip round the ear' etc as though somehow returning to that kind of approach would solve our social problems. Society is different than it was 50 years ago. The young parents I know are child focussed, the children loved and cared for and no they're never hit. Hitting hurts physically and emotionally.
Is it possible to remove a topic from "I'm on"
By special request, let’s discuss our favourite Classic Music and why?

