If I play a family member of an existing character, does my character have to be the same type?

Absolutely not. There is absolutely no correlation between family relationship and character type. What your character is and who they are is completely random - it's up to you, there is no set rule here folks. For example, a set of siblings can be a dreamer and and aspect, it's all mix and match.

Okay, let's take an example - if you're playing an aspect of the Wicked Stepmother and someone else is playing your character's daughter - that daughter does not have to be an aspect of Cinderella. That daughter does not have to be an aspect at all.