I can really only tell you what happened when I went to court... which was in NY.
First of all, check your state laws, in some states there is no such thing as partial custody. One parent has full legal custody and the other parent get visitation.
For us, we went to court with both our lawyers. The two lawyers went and met with the mediator that write down everything and submits it to the judge. Since there was suspected drug abuse our son was appointed an attorney by the court who was ordered to represent his needs. At the first date, xabf was set up with random drug testing and we were sent to a local agency that supervises visitation. That was pretty much it for the first day.
You really don't "need" proof that he's an addict. The allegation alone is enough to make the courts order drug tests and enough for them to order supervised visits.
Also, before we went to court, I wrote an affidavit of everything that had happened and had it submited to the courts. It was 25 pages long!
Hope that helps!