The subject of the sentence is "Jamie." The phrase, "as she unwrapped the presents" is an adverbial phrase that modifies the predicate "smiled."
I have smiled at you.
She crossed her arms and smiled smugly, knowing she had won the argument.
She smiled coyly at him from across the room, hoping he would notice her.
The great ape jumped off of the swing, turned, and smiled at us.
The girl looked at me shyly. He smiled shyly.
I have smiled at you.
After dropping me off in the local Walmart parking lot, the little girl smiled at me.
Smile (verb) -- I smiled at the man. Smile (noun) -- She has a beautiful smile.
I smiled as I savored her scent.
She crossed her arms and smiled smugly, knowing she had won the argument.
She smiled coyly at him from across the room, hoping he would notice her.
The great ape jumped off of the swing, turned, and smiled at us.
The girl looked at me shyly. He smiled shyly.
She smiled at me approvingly
The sun smiled down warmly on the field, brightening the flowers with its cheerful rays.
Sweetly is an AdverbThe birds sang sweetly.He smiled sweetly at her.
Is this sentence a appositive "grandfather smiled drew a breath and began the story always one of our favorites"