Full Custody and Liability

[kydad]

This is a very complicated situation so I will try to make it in a nutshell.
I have had full custody of my daughter since she was two years old. She is currently 16. My daughter has some serious mental issues. Her mother and her aunt have both been diagnosed with various mental illness and both have been hospitalized and aunt was once a ward of the state because of her severe mental problems. I guess that my daughter inherited this problem. I have tried for years and year to help her. We have seen countless doctors, counselors, etc. Tried drug therapy, couseling, group meetings, you name it. Nothing worked. My current wife has been with me since I gained full custody of my daughter. For seven years we had no other children. My daughter was enough to deal with. My wife got pregnant and gave birth to our baby daughter. My other daughter from the previous marriage officially went off the deepend. We found her trying to harm the child while they were alone together. Mostly physical abuse to the baby but some mental as well. I guess I reached my breaking point. Her biological mother has never really been a part of her life. She comes and goes depending on her current mental state. Daughter asked if she could go stay with mom for a summer visit. Normally I would say no but after the abuse I said fine. Anything to protect my baby daughter. By the end of the summer I found out that my daughter wanted to stay with bio-mom so I said yes and agreed to send her child support. I didn't find out until later that the reason daughter wanted to stay is because mom had allowed daughters boyfriend to move in and sleep with her every night. I have no proof that this is happening besides statements from several people but I know it is true because of my ex wifes reaction to it all. As much as I hate to say it, the damage is done and making my daughter move back would be a horrible mistake. We would be in constant danger. I have a million questions but I get down to the main questions I have.
Since my ex-wife does not have custody of our daughter and just has an educational type guardianship, am I libel if my daughter does something while at her house? For example: If her mother allows her to drive a car with or without a license, if she wrecks into someone, will I be responsible? Can I be sued? Am I libel for my daughters actions even though she no longer lives with me? #2 My ex wife allowed my daughter to drop out of high school and enter into a part-time diploma program. She will only be attending school a few hours a week. Can this be considered emancipation? Should I be paying child support if the child is no longer in a typical high school? And can I legally be made to pay child support when I am the one that has custody? I didn't know if it was determined by custody or where the child is actually residing.  All of this is taking place in Kentucky. Any information would be appreciated. I am worried that I could lose all that I have if ex wife allows our daughter to do something stupid.