You can't interfer in your friend's life, unless she is asking you herself. If it is the child who is confiding in you, I think you should mention it to your friend in a pleasant conversation. If the 13 year old has asked you not to tell her mother of her unhappiness, and you have promised, then please do not betray the child's trust.
If you are merely viewing this situation and drawing your own conclusions, then perhaps a frank talk with your friend about what you have noticed would be the way to go.
Adults quite often make huge mistakes right in front of us...the sane ones...but, they are adults and unless this friend wants your help and interference, I'd keep to myself.
The daughter is very young and naturally doesn't want things to change in her mother's life, but it isn't up to us to preach our ideas to the mother. Mom and daughter will work this out at their own pace and in their own time. If they don't, then it will not be your fault.