And moreover, it’s teaching the child to use violence when he doesn’t get he’s bidding.

How about a 4th option- Setting a simple ultimatum, as long as he’s making a fool out of himself, you’ll be putting whatever stuff you already got him back in it’s place.

If you can’t control your 2 year old, don’t take him shopping.

nope

Can you give an example of a mammal that uses violence against its own young (except of course for cannibalism)?

AFAIK tigers use growling to control their cubs and if the cubs behave terribly wrong, the tigress will turn her back on them or even walk away.

I searched the Internet to find any evidence of dogs or wolves biting (or otherwise using physical violence against) their offspring and could not find any. I’d appreciate a link if anyone can provide one.
I found a nice picture of a muzzle bite (wolves version of a kiss) though.
http://www.fortunecity.com/greenfield/wilderness/338...

Legitimate where? As far as I know, in the state of Israel, as well as most other countries and the United Nation Convention on the Rights of the Child, bodily harm (grievous or otherwise) as well as any form of physical or mental violence against children is prohibited.