http://www.davesexegesis.com/wp/wp-content/uploads/2006/07/Puritan%20Parenting.pdf

This looks to be a college or post-graduate level research paper on Puritan parenting practices and other general elements of the Puritan home.

Highlights from "The Uniqueness of the Puritan Ideal for the Family". 

-“The household is as it were a little commonwealth by the good government whereof God’s glory may be advanced, the commonwealth...benefited and all that live in that family may receive much comfort and commodity.” (Robert Cleaver, quoted by Daniel Doriani in “The Godly Household in Puritan Theology

-“It was the husbands responsibility to channel the family into religion; to take them to church on the Lord’s Day, to oversee the sanctifying of the entire day in the home; to catechize the children, and teach them the faith, to examine the whole family after each sermon, to see how much had been retained and understood, and to fill any gaps of understanding that might remain; to lead the family in worship daily, ideally twice a day; and to set an example of sober godliness at all times and in all matters.” (J.I. Packer, The Quest for Godliness: The Puritan Vision of the Christian Life

-Oliver Heywood described it as acting as a priest in the family, a role that consisted of the four duties of the Old Testament priest:5

1. To instruct the people in the principles of religion, and their duty to God and each other 2. To manage the holy offerings and sacrifices for atonement (confess the sins of the family) 3. To intercede for the people (to stand between the dead and the living) 4. To bless the people

-As covenants included both blessings and cursings, so children were seen as mixed blessing.7 John Robinson said that “[Children] are a blessing great, but dangerous.”8 They would affirm Psalm 127, that children are a blessing from the Lord, but that they also bring heartaches physically and spiritually from their birth until eventual marriage.

-Excessive affectionate smothering, or “doting”, of their children was looked down upon.10 They observed that even apes killed their young with hugging.11 They did not want to be cold toward their children but rather impartial.1

-Baptism, in particular, was seen as an inauguration of a child into the covenant: “[God] ordained baptism to be used as a solemn initiation of all that will come into his church, and enter into the covenant of God.”-

-They will follow thee up and down in that ever-burning lake with direful curses and hideous outcries, crying out continually, “Woe unto us, that ever we served such a wicked wretched master, that had no care of the salvation of our souls, took no course to save us out of these fiery torments!” Even thine own dear children, in this case, will yell in thine ears, world without end, “Woe and alas, that ever we were born of such accursed parents, who had not the grace to teach us betimes the ways of God, to keep us from our youthful vanities, and to train us up in the paths of godliness! Had they done so, we might have lived in the endless joys of heaven; whereas now we must lie irrecoverably in these everlasting flames. Oh! it was the fault of our own parents’ unconscionable and cruel negligence, that all our life long struck full deep in our souls, and hath now strangled them with everlasting horror.”23

The Puritan outlook is always so bleak. John obviously relishes his sons, but I'm sure he too looks on them as a dangerous responsibility. His guilt must hugely come from the fear of his sons finding out that he's committed indecencies. While it certainly his goal, I'm sure there is an subconscious Oedipal fear that they may grow to be purer men than him in action. On top of this there would be some subconscious fear that Elizabeth loves them more than she loves him. 

I opened this article wondering whether corporal punishment was a common Puritan practice, and it doesnt seem to be, which makes John's threats of whipping all the more violent and interesting. I don't believe he has ever hit anyone though. I also doubt he ever would have made those same threats to his sons. I can only assume that a Puritan boy raised to be as hard working as a Proctor would be would hardly be any trouble to raise. In fact, I suspect he has a better relationship with his sons than do many others in the village.

Johns refusal to have his youngest son Baptized is evident of his lack of faith in both Parris, but also the Puritan dogma.