I'll take a different view here. While one could surely argue that the shoe flicking didn't justify what followed, I found the take down mostly appropriate. The two or so blows after she was down were 100% out of line.
Be mindful of your feelings. They can betray you - Obiwan
Also keep in mind that if this were some other situation ..some other milieu (whatever) and a 15 year old girl reacted that way to authority, most of us would say that she needed a spanking during her more formative years.
I guess it would be more easy to understand if it was a 15 year old male. Most of us that have raised girls have known that they can only handle so much discipline before they rebel and make your worst nightmares come true. Sons, otoh, tend to run a fine line balance between fear and respect.