Can I sue my adopted family for emotional distress and negligence

Yes, it is possible to sue a family member for sexual abuse that occurred during the period when you were a child. First there is a statute of limitations that applies to your case, and the statute of limitation is sometimes suspended until the age of 18, when it starts to run again. Secondly, insurance policies that would cover the negligent party that knew or should've known of the sexual abuse but failed to intervene to stop it, may provide a defense and coverage to that third-party, But those insurance policies Often times have an exclusion for a family member who permanently resides at the residence as opposed to a family member who is visiting that residence.. So if you were a part-time resident or living temporarily at that house,  there may be coverage that you could pursue. You should discuss your case with counsel in a private phone consultation regarding all the facts and circumstances. And finally, in order to have credibility, you should at least have some kind of evidence that you can produce that would support or corroborate the claims that you were making. For example did you ever tell another person about this abuse when it was happening? Did you keep a diary of what was going on? What evidence do you have that would corroborate your claims, other than your own he said she said evidence?