Student or Learner
Mark always goes to pieces with his son.
--- Does it mean that they always have an argument with each other?
It is a phrase which has both literal as well as figurative meaning;
Literal is: something] to fall apart into many pieces.
The glass went into pieces after falling down from her hand.
All her hopes and ideas went to pieces in that one meeting.
- Figurative: for something to become nonfunctional:
Fred went to pieces during the trial
- Fig: for someone to have a mental collapse or became so upset that they are unable to control their feelings or think clearly.
He was quite throughout the funeral, but went to pieces after every one left.
The example sentence can have a similar meaning to portion underlined but as pointed out by Raymott, it dose not sound natural. I think it could be:
Mark always goes to pieces with the unbecoming/unruly behavior of his son.
It may yet be a Midlands expression for laughing intensely, having loads of fun.
You'd know better than I, but my Midlands auntie said things like that sometimes.