That does appear to be true in many households, much to the detriment of anyone unfortunate enough to be living in such a household.
Case in point, an uncle of mine.
He married a woman who had been divorced, and had a daughter by the prior marriage. Together they had another daughter and a son.
My uncle was given carte blanche to discipline the boy, and the turned out to be one of the nicest, most decent, honorable, educated professional men you’d ever want to meet.
His wife would not let him lift a little finger where the girls were concerned. “They are MY responsibility, and I will discipline them!” He was really not permitted to be involved in that aspect at all.
Of course both of the girls were complete train wrecks. Many serious issues growing up, and one of them died quite young.
For some reason women these days tend to get claws-out defensive about their daughters, which is not good.