J.W.
You stay the heck out of it, that isn't bullying. You are coloring your perception based on your past.
Lord have mercy! Mom made a 15 year old take his little sister to the park. Mom is stupid because that one is the clear outcome, the boy is taking out his frustration with the situation on his sister. The sister isn't innocent in this either. It is common sense, cause and effect. She pouts until mom forces the boy to take her, he picks on her the whole time. If she wanted to avoid being picked on she doesn't force her older brother to go to the park with her.
Heck she may even be going so far as to enjoy torturing her brother by making him go. Oh look mom loves me more, she is making you suffer for me.
You don't know. Stay out of it because that isn't sibling bullying. You probably weren't bullied either. Shame you didn't have multiple kids, as the parent you figure out this is normal behavior. You only see what your brothers did to you and not how you provoked them. I have never in my life seen sibs that actually hated each other.
After reading your what happened: Did you see the sister crying? Nope? Okay I know you have a young child so you haven't seen this yet but there will come a point where your child tries to manipulate you by crying. Total limb ripping off screams of injustice....yet with no tears. If you don't see tears the child tends not to actually be upset. There just isn't that many dehydrated children in the world.
Sorry but even with the extra information that girl was very much a participant in that dynamic.
Do you even get what happens if you intervene in that dynamic? I can only speak from a parent point of view because I never got in the middle of other people's kids. If you "protect" one that child uses it as a point to manipulate from. They learn to make sure you don't see their bad behavior and then can actually punish their sibling. That is how you get spoiled punk teens. They have never learned their behavior has consequences.
If anything I am hoping you get there is a heck of a lot to sibling dynamics and stay the heck out of it. It just isn't your place.