People are so "black and white" about these type of issues, but there is probably far more grey to it.
Firstly, no one is obligated to be friends with anyone else, and that includes children.
Friend 1 is saying her DC was bullied, but friend 2 is saying it was just normal playground behaviour. The school intervened, and separated them. That is ALL that is known. No one knows if it was really bullying.
Not all excluded children are bullied. Some are, some are socially awkward and struggle with friendships, some are just incompatible personalities, and others are right PITAs to be around.
And yet here everyone is jumping on the "poor friend 1" bandwagon.
Op, you obviously feel for friend 2. Not making a judgment on which friend is 'right' because that's not really possible. But the reality is that unless friend 2 is willing to try to deal with this hurt instead of hiding away, then the friendship group will be permanently split. She is forcing you to choose between her and friend 1, whereas friend 1 is not.
But friend 1 has also shown that she is happy to go for the nuclear option - lay it all out loudly, make the grand announcement that her DC is moving schools and THIS child is part of the reason why! There were other, less confrontational, ways of moving schools. (Eg, I know our DC aren't really friends anymore and while that may not be anyone's 'fault' and the school has done what it can it has left my DC unhappy and I feel this is the best move for them.)
Regardless of what happened, THEY are bringing playground dramas into the friendship group.
So really, regardless of the rights or wrongs, who do you want to be friends with? Because sadly I don't think you can be friends with both.