One great source of stories for any speaker is their own family history. We all have stories that we can tell to illustrate any point we want to make.
The problem is that you as the speaker know the story intimately while the audience knows nothing of the people or the circumstances surrounding the story. Your difficulty comes from trying to put in enough details to tell the story but not too many details. This is where revision and editing are important. It is best to practice your story in front of another person and have that person judge your story; too many details or too few. Your evaluator can also tell you which parts of the story are significant to your audience.
Start is by listing your family stories in a journal. Write down what you remember about the people, places and situations. Then begin to edit and revise.