I don't think family drama is necessarily an inappropriate choice. I'd just be careful how you frame things. Remember that they're not just looking to hear about what happened to you, but also how you responded to those events, so if your response to these events doesn't paint you in a good light, it may not be the best choice.
For example, I have some challenging family history things as well, but I generally avoid talking about them in interviews because I recognize that it's hard for me to talk about them without sounding bitter. When choosing what topic to use, I'd think about if this is something that you can comfortably and objectively speak/write about in a professional way.
