Paul’s words to children here are a reminder that they were present in church services, and that it is appropriate to have something said to them (we do it mainly by a children’s talk). Obviously, the children he has in mind are old enough to understand his teaching.
From his words, we can see that parental requirements should be consistent in that both make the same rules for their children. Further, the obedience is to be comprehensive (in everything), which I would take to be a reminder to parents not to make unnecessary and unrealistic demands of their children that they would find impossible to obey.
In particular, Paul addresses fathers in Colosse and he wants them to realise their responsibility in maintaining a congenial atmosphere in the home so that the children will follow the faith of their parents rather than becoming angry at it.
The provoking to be avoided is that which comes out of unfair discipline. I recall reading a story of Horatius Bonar. His son had been caught by a neighbour climbing on some rocks in search of birds’ eggs. The furious neighbour marched Bonar’s son to his house and said to Bonar, ‘I hope you give him a sound thrashing.’ Bonar replied, ‘If I thrashed the boy for that, what would I do if he told me a lie?’
The son later gave this testimony of his father: ‘So skilfully did he exercise his guidance as a father, that I never felt the rein that was driving me. I admired his strength and firmness, and as a schoolboy I felt him to be always absolutely fair. He laid himself out to be approachable, and he continually invited my confidence. He liked me to tell him everything, and he was easy to come to.’