What does the trembling of the mother's hands symbolize

Possibly all the trials and tribulations experienced throughout her life.

Explanation:

In Morley Callaghan's short story, "All the Years of Her Life," Mrs. Higgins' trembling hand represents all of the trials and tribulations of her life. Although she is able to remain outwardly calm under duress, after the fact, her trembling hand signals the release of her emotions.

Symbolization is a very vague subject so it is due to interpretation.