You need to hire a family court attorney in your area to file a motion in Family Court to make the judge aware of these facts and seek relief.
I am trying to give you a general answer to your question. We do not have an attorney-client relationship by this response on the avvo website. I have not been retained to represent you. I am licensed to practice law in Kentucky and in federal court in this state and the Southern District of Indiana. You need to seek legal advice from an attorney licensed to practice in your area..
I don't know about Kentucky law but in California (and it is probably similar there) the facts you report are absolutely grounds for only supervised parenting time. Those facts are also grounds to compel the father to be assessed for alcohol addiction and be forced to attend AA meetings. please see a family law attorney in your area for some help to protect your child.
Yes, the family court can issue an order prohibiting. You should first talk to social services. A problem in many cases involving alcohol is that alcohol consumption is very difficult to monitor and you don't want children acting as monitors.
Kentucky law does not certify specialty of practice in this area. The advice given herein is informational and should not be considered as creating an attorney/client relationship. Michael Bouldin is an independent attorney located in Northern Kentucky. It is strongly recommended to not give any confidential information on any website.