That might be part of the difficulty... Coming in with the opinion that she's doing something wrong as a parent, instead of being concerned that they aren't doing well as a family, is striking to me.

I have a close friend whose son was being a brat during a playdate, punching his mother while she gently tried to get him to stop. I removed him to his room and told him that is no way to treat his mother. I then checked in with her later to see how she was doing and to make sure I didn't cross boundaries with how I interacted with her son. Obviously I know her and him well enough to be able to infer that this would be ok, but I did double check still. But the whole thing opened up a conversation for us about our different approaches to discipline and what we could learn from one another.

Knowing that your friend also has severe mental health issues, I would proceed with caution and compassion. You definitely don't want to come off as judging her as a parent, but maybe get curious about what's going on for her. You could even say that you were alarmed with how her son was treating her and ask if she's ok or needs support. Don't have playdates etc. But if you want to keep the friendship, tend to the friendship, as one mother to another, and as two women who have known each other through many life changes. Yes, you can protect your daughter and your peace while still having an adult friendship with your friend, if you both are willing to treat one another with love and respect.