My father doted on my younger brother like a precious gem in his palm.
Literal
Father [topic-は] my younger-brother [object-を] palm's gem [like-のように] loved.
掌中の玉のように (like a jewel in the palm of one's hand) is a literary simile for cherishing someone dearly — treating them as precious and delicate. かわいがる means 'to dote on, to shower with affection.'