yes, i would have done the same thing. if the kids were the same age, i leave them to sort it out between themselves, unless the violence passes a certain level! but if one is younger/weaker than the other, or is getting upset, i intervene. i let them fight it out unless it crosses that line into bullying - which from your post it sounds like it did.
apple doesnt fall very far from the tree imo, so if the kid is a nasty piece of work, why be surprised when the mum proves to be too?
you protected your son from a bully, you challenged the mum, albeit you didnt get what we would consider an appropriate response - but like i said, if she was a good and caring parent, would her child be a nasty rude brat?
you did everything you could; deep cleansing breaths and be happy your child is a nice person!!!!