Based on your assumptions - we have zero idea what happened or what was said. And No, I'd not class a bit of shoving as assult in this context based on the very little informaation that has been provided.
Words can be assult, words can also be litigious much like most of the utter crap responces on here. The very same people moaning and calling this assult are the very same people that would moan about people being locked up over Twitter posts. 🙄- Cake and eat it comes to mind.
For all we know the son, was physically threating dad, for all we know dad is 5ft and 9 stone wet through and son is 6ft 10 strapping lad who could easily hurt dad.
And again we don't know dads history, for 14 years he's been around, until a divorce, agian we have no idea why, mom could have been shagging the milk man for all we know, dad could have been heart broken his family has been turned upside down. OP never said he was a deadbeat dad who had no intrest in their children.
I do tend to agree that dad needs to offer the first olive branch so to speak, but agian we have no idea what was said or really happened.
Ask yourslf, whats the worst thing you could think of your children doing, that would warrent this responce? and agian, this would be a very personal as we all have very different views and break points. This could be anything from words, assult, drug use and a hundred things inbetween.