Any ideas why she gives this one child special privileges over the others? I'd feel curious about that and approach her in a "I would like to understand" way. Maybe something happened that you don't know about and that's why she's doing what she's doing. Be a friend and support her by understanding her situation first, then you can talk about the problems it's causing. This is not about anyone else imposing their child rearing skills onto her. (I'd feel hella pissed about that.) There has to be some trade off she's getting for letting this child do more than her other children. There's a reason for it.
Seek first to understand. It may completely change your mind about the whole situation when you see it through HER eyes.
Words might look like:
Me: Hey Betsy. I'm noticing that you've switched schools for Susan and a few other things are going on lately. I feel concerned. I see friends backing off and I imagine that might feel lonely for you. Would you like to talk? I'd like to listen if you want to talk about what's going on.
Betsy: Yes, I feel so mad at these people judging me about how I treat Susan. Screw them.
Me: Judging feels terrible. I don't want to do that either. Any idea why it's happening?
Betsy: They just think I let her have her way. What they don't know is that she has a life threatening disease (or she almost died at birth or I had postpartum and nearly killed her by shaking one night, etc.). So I give her a lot of extra leeway.
Me: Oh wow. I didn't know that about Susan. That feels horrible. I'm sorry Betsy. I feel bad. I have been concerned about Susan's behavior and it's impact on me and my family. I had no idea. Is there anything I can do?
And on and on and on...
Seek first to understand.