If you have to beat a kid or stuff hot sauce down his throat to make a point then you trivialize normal behavior.
What if she's out of hot sauce?
Does she have to go to the grocery store to get her next stock of parenting equipment?
What would be her next parenting weapon choice?
Absolutely this is child abuse. I had this done to me as a young teen by my mother, but she put it in my eyes.
She had my older brother hold me down and put drops of tabasco in my eyes.
That was one of her milder forms of abuse.
Anyone that would excuse this kind of behavior is sick.