From the Super Mario Wiki, the Mario encyclopedia
The Mother Penguin is a penguin who appears in Super Mario 64 and in Super Mario 64 DS in Cool, Cool Mountain. She has lost her daughter, Tuxie, so Mario goes to look for her. Once Tuxie is rescued, the Mother Penguin rewards Mario with a Power Star, completing the Li'l Penguin Lost mission.
If Mario brings her another baby penguin, the Mother Penguin will not accept it. She insists that this baby penguin is not her daughter and that they look nothing alike.
If Tuxie is taken back after being delivered to the Mother Penguin, she follows Mario with a cross expression until he drops Tuxie again. However, she does not seem to react in any way if Mario gets far enough away or drops Tuxie off the edge.
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