What does the Pali canon, and other respected work, teach about parenting, particularly early fatherhood? In particular the many possibilities for dukkha which arise?
It teaches that birth is suffering for the reason that it is like entering into a binding contract:
One goes through all these sufferings simply because one happens to take a new existence. Accordingly, jāti, re-birth, being the foundation of all the miseries of the whole existence, is defined as dukkha by the Buddha. A careful consideration will confirm the accuracy of this definition. Re-birth is really dreadful like signing a document which later will give rise to complications. Thus jāti is dukkha because of its dreadfulness. To summarise, the physical and mental afflictions are occasioned (arise) because of jāti in each existence. Only when there is no more re-birth will there be total release from these inflections. Thus the Blessed One had taught that the very origination of new existence, jāti is suffering.
It teaches that children have power over their parents:
Bhikkhus, there are these eight powers. What eight? (1) The power of children is weeping; (2) the power of women is anger; (3) the power of thieves is a weapon; (4) the power of kings is sovereignty; (5) the power of fools is to complain; (6) the power of the wise is to deliberate;"" (7) the power of the learned is reflection; (8) the power of ascetics and brahmins is patience. These are the eight powers.”
AN 8.27 (Bodhi, trans)
It teaches that a parent has responsibilities towards their children:
"In five ways, young householder, a child should minister to his parents as the East:
(i) Having supported me I shall support them,
(ii) I shall do their duties,
(iii) I shall keep the family tradition,
(iv) I shall make myself worthy of my inheritance,
(v) furthermore I shall offer alms in honor of my departed relatives.
"In five ways, young householder, the parents thus ministered to as the East by their children, show their compassion:
(i) they restrain them from evil,
(ii) they encourage them to do good,
(iii) they train them for a profession,
(iv) they arrange a suitable marriage,
(v) at the proper time they hand over their inheritance to them.
"In these five ways do children minister to their parents as the East and the parents show their compassion to their children. Thus is the East covered by them and made safe and secure.
It teaches that parents are meant to be helpful to their children:
“‘Brahmā,’ bhikkhus, is a designation for mother and father. ‘First teachers’ is a designation for mother and father. ‘Giftworthy’ is a designation for mother and father. For what reason? Mother and father are helpful to their children: they raise them, nurture them, and show them the world.”
AN 3 (Bodhi, trans)
It seems to suggest that children might are an impediment to attainments higher than stream-entry:
Sitting to one side, the lay follower Dhammadinna then said to the Blessed One: “Let the Blessed One, venerable sir, exhort us and instruct us in a way that may lead to our welfare and happiness for a long time.”
“Therefore, Dhammadinna, you should train yourselves thus: ‘From time to time we will enter and dwell upon those discourses spoken by the Tathāgata that are deep, deep in meaning, supramundane, dealing with emptiness.’ It is in such a way that you should train yourselves.”
“Venerable sir, it is not easy for us—dwelling in a home crowded with children, enjoying Kāsian sandalwood, wearing garlands, scents, and unguents, receiving gold and silver—from time to time to enter and dwell upon those discourses spoken by the Tathāgata that are deep, deep in meaning, supramundane, dealing with emptiness. As we are established in the five training rules, let the Blessed One teach us the Dhamma further.”
“Therefore, Dhammadinna, you should train yourselves thus: ‘We will possess confirmed confidence in the Buddha … in the Dhamma … in the Saṅgha.… We will possess the virtues dear to the noble ones, unbroken … leading to concentration.’ It is in such a way that you should train yourselves.”