Hi! I can understand why you might want to know the origin of your issues. You seem to want to come at your problems from more of a psychoanalytic perspective. However, ultimately it doesn't matter why you are they way you are, does it? The goal is to get treated for these problems.
I would stick with your therapist's suggestions for right now. Don't worry so much about the past. You can't do anything to change it. Be concerned about changing your feelings and behavior now.
If memories come up, then you can be aware of them. But in general I suspect you already see how you were reared, and you can just generally attribute most of your issues to that. For example, you ran away from home because you weren't happy there.
You probably don't like my answer, but I do think the present would be best to concentrate on! Your therapist sounds like she is willing to meet you halfway, though, with the new approach she's suggesting.