In a stable upbringing, should both parents have authority?

There was a case of a rebellious teenaged 15 year-old son. The lady's husband unfortunately passed away in an accident and after several months, the child became out of control. He would tell his mother ''dad's not here anymore so therefore you can't do anything''.

When the father was alive, he wouldn't dare disrespect others nor his mother. However, the mother had no style at all and was super passive. So when the father died, he rebelled.

I find it wrong when only one parent has authority and the other is a pushover, all passive and does nothing. In a normal upbringing, shouldn't that kid's mother also have authority?

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Unfortunately there isn't any other male figures in the family to correct him. The deceased husband was an only child and the mother only has 2 sisters, brothers.
In a stable upbringing, should both parents have authority?
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