Charlotte's father is a man of rules and order who thinks punctuation and spelling are very important things for his daughter to learn. He is, after all, the one who gives her the blank book that serves as her journal. Mr. Doyle is also the one who sends Charlotte across the ocean in the first place (it's his company that owns the ship) and she thinks of him constantly during the voyage. Captain Jaggery, for example, reminds her of her father (5.48). Both men are fathers, businessmen, and they both really, really, really love order. Really. Also, Charlotte is always asking herself what her father would or would not do if he were on the boat. When she decides to apologize to the captain for flicking him with the whip, for example, it's because she thinks that's what her father would want her to do (12.67).
In the end, though, Charlotte's father is not as full of truth and justice as she might have once believed him to be. He doesn't believe the account written in her journal is true. What's worse, he actually burns the journal. Because of this, Charlotte decides to leave the life of rules and order her father represents and return to the sea.
As for Charlotte's mother, well, she has a very small role in the novel and is generally an accessory to Charlotte's father. She is, of course, horrified by Charlotte's appearance when her daughter arrives in Rhode Island (22.61), but other than that, Mrs. Doyle doesn't have a whole lot to say in this novel. Why do you think this might be?