Our expert says:
A "mother figure" need not be one's mother - but someone who by the way they act, demonstrates how a good mother functions.
Unfortunately, though, it seems that your father has failed this younger sister, and his long-term gf doesn't seem to have been helpful. If he genuinely doesn't know what to do with her, he could have asked welfare and child welfare organizations for advice and help.
You are right to establish clear rules if she is to stay with you, and again, if she is supposedly going to school, her problems should be discussed with the principal and maybe a school psychologist involved to work with her. And the rules must be applied - she needs to be reminded that she is not doing you a favour to allow you to help her, and that one rule is that she needs to be polite and communicate pleasantly and inform you of problems that need to be dealt with.
"letting her do what she wants to do" ( which would be a decision of despair ) would be saying that all she wants to do is good and OK, which it isn't. That's not the same as facing the fact that you can only go so far in trying to help, and if she refuses to work with you ( and anyone else enlisted to help ), she can't be helped. Nobody can take that responsibility away from her.
It is not your fault that she didn't have a mother around, and this fact ( which is sadly a very common situation ) does not have this effect on most children, and is not excuse for the bad choices she is insisting on making.
Being concerned is appropriate and natural, but it should not amount to blaming yourself for what she does - you cannot behave well on her behalf, and none of this is your fault
Purple's comments are useful, and she makes the important point that you and your other sister have grown up to be responsible citizens. The route your sister is insisting on taking is her own choice, and was never inevitable
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