During college, one of the jobs I took to support myself was as a cashier at Chuck E. Cheese. The store I worked at wasn't the dinky ones you see now...it had two dining areas, huge animatronics, and a full arcade. Occasionally the manager would call on me to be Chuck E. for a birthday party...or the occasional scheduled "surprise" appearance that was part of the animatronic show.
Having a "guest" punch the nose, pull the ears, tug on the costume, make inappropriate sexual comments, etc. was a pretty regular event. Usually, it was just annoying. But, in some cases it was painful. I had bruises on my face more than once from the punching...one of my coworkers who wore glasses had a huge cut.
What you see and hear in the White Rabbit video is the father egging his daughters on. They follow daddy's order, and harrass the character. I don't know if what they did was painful or just annoying, but it was surely unneccessary.
I agree that the characters should have handlers 100% of the time. Anyone over the age of 5 who hits, pulls on, pushes, etc. a character should be given a warning. If they persist, they should be asked to leave the park. If the trouble-maker is an adult, they should be charged with assault and banned from the parks.
Their behavior not only affects the character, it ruins the experience for those waiting in line.
Unfortunately, there's no law against being a boor or an idiot...and, while what the CM did was out of line, people who choose to entertain themselves by annoying and bullying others shouldn't be surprised when the people they are bothering react!
The family in question was waaay out of line. If they were just acting stupid, as opposed to actually being stupid, maybe they learned something from this!
I'd add...if you encourage your kids to purposely do things to annoy, bother, or bully others, you shouldn't be surprised when someone who has common sense (since you obviously don't!) teaches them the lesson that they should have learned from you! The world isn't going to give your kids a break because their parents are idiots!