in the palm of (one's) hand

Under one's total influence, domination, or control. She now has the entire company in the palm of her hand. Sheesh, he's got his parents in the palm of his hand. Money can get you almost anywhere, so if you want someone in the palm of your hand, don't be afraid to spend freely.

in the palm of your hand

If you have someone in the palm of your hand, you can control them, and they like everything that you do. A quick look at the audience shows that she's got them in the palm of her hand. The girl clearly thought she already had him in the palm of her hand. Compare with have someone eating out of the palm of your hand.