My baby always looks for me when she's with her mother. But when I carry her, she starts to cry and wants to go to her mother. What can I do to make her stay longer with me?

This is very normal as baby sees your wife for longer hours and has separation anxiety towards your wife. My husband also my kids' playmate only and they will still look for me when they suddenly 'remember' me. What you can do is, spend alone time with baby without your wife's presence. When I am around in the house, my kids will stick to me too but when I am not around they turn to daddy.