I think it's horrific that anyone would do that to a two-year-old child, and more horrific that anyone would try to excuse it. We are not talking about "three whacks on the butt" here.

He dragged the child by her neck. He hit (spanked, for those who want to sugarcoat it) her three times, and the OP did NOT know if it was on the behind or somewhere else as she could not see them at that time. He shoved the child back towards her mother. That is physical and emotional abuse.
He assaulted and terrorized that child. I don't give a flaming rip who disagrees with me, either. I won't even be debating it on this thread, because there's no point. The same people always excuse or condone it, and bring out the usual pro-spanking arguments.
Hitting a child is ALWAYS wrong...but this was downright abusive. I would have stepped in immediately and
called the police and/or child protective services had I witnessed the same incident (yes, really). DRAGGING HER BY HER NECK??? You have got to be kidding me!!!

This is my MAJOR hot-button issue. It sickens me how people will defend corporal punishment--no matter how young the child, no matter how severe the assault, no matter how terrified the victim. IT'S WRONG. PERIOD. Ugh.
I'm sorry you had to witness that, OP. I know it's frightening. Next time, I'm sure you will speak up! Don't beat yourself up about it.
Oh, and since I am being totally candid here...
He gave her quite a few chances? Not to be
physically attacked by one of the two people who should always keep her safe? And she blew it, so that makes it okay to
assault her? I want to vomit just reading those words. Truly.