"The Christian Father" (written by a German Catholic Bishop) may be of use, as it addresses, in its entirety, the role of a father in the home: https://archive.org/details/thechristianfath00cramuoft/page/n3/mode/2up
Fr. Michael Müller, C.S.S.R., in one of the volumes in his series "God the Teacher of Mankind", addresses in great detail the duties of parents which includes education of the body and the soul, the power of good example to little ones, punishing, etc. https://archive.org/details/godtheteacher05meuluoft/page/n115/mode/2up
Here are some enlightening excerpts from p. 114 and 115 that applies even to babies, and more so to toddlers:
As to the Christian instruction of children, it may be said to begin from the moment in which they open their eyes and ears to the sights and sounds of the world about them; and of these sights and sounds those of the mother are the most impressive and the most enduring. It will be easy for mothers to impress the truths of our religion upon their children if they are careful to prepare the soil which is to receive the seed of the word of God. "The seed of the word of God that fell upon good ground sprung up and yielded fruit a hundred-fold." (Luke viii., 8.) This good ground is the good natural qualities transmitted to children by their parents. There is a child. Look at it. Is it not the image of the father, the same hair, etc.? In the same, though more striking manner, parents transmit to the child their dispositions for good or evil. There is a mother. She is of a calm, meek and charitable disposition; she is very religiously inclined, and full of the fear of God. Now, as a rule, we notice the same turn of mind in her children...
A certain young man had a great love for virtue: he was extraordinarily pious, whilst all the other members of the family were very indifferent to God and religion. He entered a religious order, where he led a holy life. How did it happen that he was not like the rest of the family? Next to God's grace this fact was owing to his mother, who, some time previous to his birth, was strongly impressed with the fear that she would soon die. So she prepared herself for death. She gave herself up to prayer as much as her family duties allowed her; she went to Mass every day, often received the sacraments, and gave alms to the poor according to her means. Her pious disposition was thus transmitted to her child.
We read in the life of the great Pope, St. Leo IX., that he was born with his body marked all over with little red crosses. This was attributed to the intense meditation of his pious mother on the Passion of our dear Saviour Jesus Christ.