Is what the father did a sin against his child because he deprived him of his mother, and if so, what should he have done to save him from an upbringing that contradicts his religion?

What you did with your son is the correct solution, as leaving him under the control of a non-Muslim mother will raise him upon her corrupt creed and ugly morals, and feed him with unlawful things. This poses a danger to the future of the child's religion and morals. There is no injustice to the mother in this; for safeguarding religion is more important than observing the rights of parents if they conflict with religion. Perhaps the doer of this deed will be rewarded for it, as he fulfilled his duty and responsibility towards his son, in accordance with the Almighty’s saying: ﴿O you who have believed, protect yourselves and your families from a Fire﴾ (At-Tahrim: 6).