When I was rude to him, my father's face turned bright red with anger.

Literal

Father [topic-は] I [subject-が] him [to-に対して] rude behavior took [when-とき], anger [with-で] face [subject-が] bright-red became.

怒りで顔が真っ赤になった — anger (cause with で) made his face (subject が) turn bright red (真っ赤). 失礼な言動 (rude behavior) is a formal compound.