As far as I know the doctor under gurumaas influence switches the babies, since she know Khushi is going to go to australia, and she wants the evil one near her. She wants to get all the powers by herself.
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Mahir and Timir have special powers where they can read peoples mind etc. That is how they know who their real mother are. Also Khusihi's both mothers find out when the doc who did the switch confesses or talks about it. 😊