Just for clarification, Munchausen is when one makes herself sick just to get rescued and Munchausen by Proxy is when someone makes someone else sick just to save him/her.
What part of the situation are you giving the attribute of one or another? From what I understand out of your post, your friend has the Chiari but suffers more from the symptoms than her brother or mother. This might be making her rather an hypochondriac in my opinion, if you doubt the severity of her symptoms or the illnesses of her children. In addition, children might be trying to get some attention by acting out or acting sick as this is the only way their mother gives them desired attention.
I don't see how this boy's bipolar disorder would be caused intentionally by someone else. And as you say the doctors haven't found anything wrong with the girl. So she might be faking the pain, but it is rather alarming that they are giving her the meds for non existing diagnosis. I hope it's a placebo!
However, I can imagine the life in the family being psichicly very stressful which may cause phantom pains or altered behavior.
Having said that, as a kid I was administered into the hospital with severe abdominal pain due to undetected irritable bawl syndrome, just to be released with no diagnosis. After several hours I'd be feeling fine again but my IBS was caused by stress which was plenty around in my family, so the pain would reoccurre again, and I'd be again fine after a while. So the girl might be affected in some similar way due to potential high levels of stress.
But Munchausen syndrome, by proxy or not, from what little I know about the situation of this family, I'd say it rather isn't the case.
I am sorry your friend is in this situation, it must be hard for you to watch them suffer!
