Beating your children is explicitly encouraged in the Bible.
Partially correct, the best match is Proverbs 13:24:
"Whoever spares the rod hates his son, but he who loves him is diligent to discipline him."
While hitting your children with a rod is well classified as beating your children, I don't think the literal meaning of discipline as exclusive beating is the proper interpretation.
However, the New Testament overrules the Old where conflicts appear (for christians). In it Paul says in Ephesians 6:4:
"Fathers, do not provoke your children to anger, but bring them up in the discipline and instruction of the Lord."
and Colossians 3:21:
"Fathers, do not provoke your children, lest they become discouraged."
"Provoke" in these cases is commonly interpreted as literally "making the children angry". Which is then derived into disallowing discipline without good reason.
Therefore the convention is that discipline is in fact encouraged, but must have good and valid basis that the child understands.
Therefore, violent corporal punishment is not forbidden, nor explicitly encouraged. Disciplining your children is expected, but that does not have to be violent.
Most of those people (hopefully) know that just because you are allowed to do something does not mean you have to do it.
To bring it back on-topic, beating your wife at all is expressly forbidden, also in Ephesians 5:33 :
"However, let each one of you love his wife as himself, and let the wife see that she respects her
husband."
You are encouraged to read around the listed quotes, since they touch on similar subjects.