I'm learning the -ing clauses and I have a question about an explanation on this website:
(1) When one action happens before another action, we use having (done) for the first action, for example, "Having finished her work, she went home."
(2) If one short action follows another short action, you can use the simple -ing form (doing instead of having done) for the first action, for example, "Taking a key out of his pocket, he opened the door."
My question: Is it optional when we use "having" or "doing" in both cases (1) and (2)? Is "Finishing her work, she went home" possible, too? Or, are the two actions of "finishing work" and "going home" not short enough?