。
She quietly slipped some money into her son's hand.
Literal
She [topic-は] son [genitive-の] hand [in-に] gently money [object-を] caused-to-grasp.
握らせる is the causative of 握る ('to grasp, clutch'); paired with 手に, it gives the literal 'caused [the money] to be grasped in [his] hand,' i.e., 'put it into his hand to hold.' そっと ('quietly, gently') is a 擬態語 for unobtrusive action — the same root that gives そっとしておく ('leave alone'). The whole image is of a discreet, perhaps secretive transfer of money.