Should You Discipline Other People's Children?

I attend a weekly "Music Together" class with my 15 month old daughter, Lily, my sister-in-law, and nephew.  It has been a fun way for my SIL and I to get together weekly, as we often meet for coffee before or after class.  It has also been a great way to get the cousins together since, let's face it, life can be really hectic and finding time for such get togethers can be tricky, especially if you have multiple kids.  At this morning's class, a new mom and her two boys appeared.  One boy was an infant.  The older boy looked to be about two or three years old.  The older boy was a bully.  He spent a good deal of time during class harassing the other children to various degrees.  Those of you who are familiar with the "Music Together" program know at some point in each class there is a "play-along" song where the children are invited to pick their own instrument from a wide variety (usually spread on the floor in the middle of the circle) and "play-along" with a song.  Lily picked up a pair of finger cymbals and sat in front of me while I shook a tambourine.  The bully came over and grabbed one of the cymbals out of Lily's hand.  Without even thinking, I grabbed the cymbal back from the boy and said, "Lily is still playing with this, but you can have it when she's done."  He looked and me and slid back on the floor.  No response from the mother.  I went so far as to make good on my word, and when Lily found herself another instrument, I handed the cymbal to the boy, saying, "It's your turn now."  He took the cymbal and moved on.  Later in the class, the boy found himself a seat on the bottom of a nearby wall unit, along with a few of the older children, whom he proceeded to push, kick, and poke, until they cleared out, leaving him alone in his spot.  This time Mom gave him "a look" from across the room and politely asked him to return to his spot next to her.  He ignored her.  Mom did nothing.  

I was INCHES away from getting up and addressing the issue myself.  But I was torn since Lily was not  directly involved.  I even found myself tempted to trip this boy as he ran past me in the circle!  Clearly that would not have helped, but I was so angry!  To quote Peter Griffin, of televisions Family Guy, it really "grinds my gears!"  This boy's mother saw quite clearly what this boy was doing and didn't find it necessary to even get up from her spot on the floor.  If one of my girls ever got physical with another child, not only did I address the behavior immediately, I also addressed the other parent, offering an apology, or having my daughter apologize directly to the other child, depending on age.  

I just cannot wrap my brain around this mother's response - or lack thereof.  What was going through her mind?  Based on his repeated abuses, I think it's safe to assume that this type of behavior is a regular occurrence for this boy.  And since there appear to be no repercussions for him, it seems logical that he would continue to bully and torment.  The parents of the other children involved did get up and remove their children from the bully's line of fire.  I'm disappointed that one of them did not address the boy or his mother directly.  I'm not sure if I'll be able to hold my tongue next week.