Keep someone on your head
That is the translation of Hindi idiom that if you keep someone on your head, you love and excessively treat them.
For example:
When you come home too late, and your mother starts to scold you, but your father speaks in favour of you: “It happens, that’s his life. Let him live the way he wants.” But your mother again says to your father, “You have kept him on your head.”
If we wish to say that person A always indulges person B and invariably forgives their transgressions, we can say that person A lets person B get away with murder.
get away with murder
PHRASE
If you say that someone gets away with murder, you are complaining that they can do whatever they like without anyone trying to control them or punish them.
[informal, disapproval]
His charm and the fact that he is so likeable often allows him to get away with murder.
Merriam-Webster defines it:
**2 : *to treat with extreme or excessive care or kindness
It's usually a negative expression that means to be too kind to someone who either doesn't need it or is being harmed by it.
If can also refer to extreme kindness towards something that really needs the care, or isn't going to be harmed by it, like a newborn baby, a pet or a business.
In your context, the wife could naturally say, "You always coddle him!!" This suggests that the father is being too kind, that their son doesn't need that much kindness, and probably that the father is both undermining her authority as his mother, and spoiling him.
