As the above expert stated, a dependant relative application is extremely difficult (if she is under 65), even with your dad supporting the application since they are divorced and thus not in a subsisting relationship.
It would be a stronger application to apply on the basis of your sister if she is British as she is aged under 18. If your mother waits to apply until she is over 18, then this will be as difficult as the above application.
The application should be made in the UK (whichever of the two you opt for) and her passport will need to be submitted with this. If she requests her passport back and returns to Pakistan, the application will come to an end. She can remain in the UK whilst her application is being considered.
The relevant case and guidance for this application is as follows:
If refused, she may have problems in the future if applying for a visit visa or coming back on a visit visa, as the UKBA may think she intends to settle in the UK. She would therefore need to prove that she intends to return by showing commitments in Pakistan at that stage and that the circumstances have now changed so she does not wish to remain in the UK.
I would certainly advise you to get legal representation with any application in the UK since it will be complex and the legal issues will need to be covered thoroughly.
I hope that helps. Please let me know if you would like further information or clarification.
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