there may be contexts in which we could say 'the' here, but it is never wrong to say 'her' and fairly awkward to say 'She opens the right hand' my brain wants to finish the sentence, 'right-hand door'? or the right hand to what? it sounds like it might be a metaphor coming? perhaps in your dialect it's always right to say the in this context, but English isn't generally like that.
The girl thinks she's caught one, but feels nothing within her fists. Cautiously, she opens her right hand. Empty. Slowly, she opens her left and there, in her palm...
As the train starts to pull away, Ella blows a kiss to her daughter through the open window. With a smile her daughter "catches" it, she opens her right hand and holds it to her heart as the train takes her mother out of sight.
She finds herself face-down with her hands underneath her. As she raises her head and tries to get up she realizes her left arm is numb. Painfully, though the other side feels bruised and tingly, she opens her right hand and spreads her fingers to reach for...
It occurred to me that you might have interpreted this as opening the flesh of her hand, which would reveal blood, muscles and bone. It could mean that, I suppose, in the right context. But most commonly it just means she unfolded her fingers either too open her fist or to allow her to hold on to or be given something.
I hope this helps.