I'm not sure what you're referring to as a not-so-happy family life, so this reply will be rather general (feel free to PM me if you want more detail). I think that writing about an unhappy family life is a difficult thing to do. On the one hand, it can be seen as whining. <img border="0" alt="[Pity]" title="" src="graemlins/pity.gif" />
However, if the experience truly shaped your life and influenced your interest in medicine (for instance, you grew up around alcoholism), then it is something you should write about. You'll need to walk a fine line between sharing too many specific personal details (which the Adcomm doesn't want) and being too generic and losing the punch of your story. One way to do this is as you mentioned: to relate the experience as a starting point and then tell what you did with it (in this same example, did you participate in Al-Anon, volunteer in any capacity with other alcoholics, etc.).
Good luck!
