Just as my father was about to leave, the phone rang.
Literal
Father [subject-が] go-out about-to-do just-at-that-moment [at-に] telephone [subject-が] rang.
~ようとした矢先に means 'just as one was about to X.' 矢先 literally means 'arrowhead' — the very tip of a moment. This idiom captures the precise instant before an action is interrupted.