I discussed similar issues in my essay. My take is you do indeed need to be very careful, but if these factors are very important to who you are and why you want to become a physician (as they were to me), it's hard not to discuss them and probably undesirable not to.
The focus, though, needs to be on what you learned from these experiences. Don't harp on them, and treat them maturely. Show that you've grown from these experiences by the way in which you discuss them. It's very easy to give off a sense of immaturity and a lack of sophistication when discussing very personal issues, and the people reading your essay will be able to detect insincerity (and on the flip side, sincerity).
Weave them into a larger narrative of your "story". Include other experiences and interests, and tie them together - you don't want the personal statement to be boring, whiney, or childish because you incessantly vent about something personal. If you show a relationship to other experiences, thoughts, interests, you'll be reinforcing what you learned from these hard aspects of your family life.
Also, I think I made the mistake of harping too much by repeating and elaborating on some of the same issues in secondary essays. My advice there would be to try and give as broad a picture of yourself as possible over all the essays that might be included in an app - write one about an experience as a counselor, or your love of a certain sport, but not all of them about these family issues. Certainly, if there's a pointed question where the answer only lies within the realm of these issues, go for it, but otherwise it might be good to diversify.
Lastly - get it reviewed by people you trust with these personal issues. You absolutely NEED other people's perspectives to help you address these issues in a way that resonates positively with a complete stranger.
Feel free to PM me, I would be glad to help in any way possible.