What does the phrase 'holding in the palm of hands' in chinese mean?
The common word is  掌握 (hold in one's palm) meaning " have possession and control of something"


Example: 

掌握軍國大權 (hold control of the government and the armed force)

掌握有力證據 (holding/ have possession of powerful evidence)

There's also an idiom 
玩弄於股掌之上 (to toy with someone on one's thighs and palms)- meaning: " play someone like a fiddle"

Another idiom mentioned "in the palm" is  "掌上明珠" (pearl in one's palm). It means " treasured daughter"