Hmmm...I feel we are not getting the whole story here. NO...I have never heard of a judge telling someone they cannot have a relationship for the remainder of their child's childhood. Nor would it be something that could be enforced. Now...he could tell you not to have a relationship during the divorce, or custody hearings, or during a period of time. This may be so the court can determine if you are willing to put "romance" on hold for the sake of your child. Usually, your attorney will tell you that. There is obviously much more to this story since you also state that you must remain gainfully employed and can't see anyone with alcohol related problems. But why would a judge tell you not to date 'anyone' and then tell you not to date a man with alcohol charges. It sounds to me like you have already dated someone with alcohol issues/charges and that situation is being corrected by the court. People do make mistakes and can recover from them but the court is interested in the well being of the child and obviously someone with an alcohol problem is NOT inthe child's best interest.
Here's a question for you...why are you being "told to work full time?" It also sounds like you may have not been working and may be unable to support your child.
Honestly, unless you can supply further details, it sounds to me like YOU have some issues that the court is addressing. Maybe you have been in more than one relationship and the court doesn't see stability. In the event that a person skips from one man to another, or gets involved with someone the court considers unfit, in a CUSTODY CASE, the judge can and will ask that you refrain from a romantic relationship. That is so your focus is on your child/ children. It can't be enforced by jail time but the court can remove your mutual custody and give custody to the other parent.
I think you need to step back and carefully consider what the court is asking of you if you value the joint custody you now share. I know someone who was in a similiar situation and she lost custody of her children. In her case she would go from guy to guy, could not hold a job, and the judge asked that she not date, get a full time job and remain employed and show that she could, in fact provide a stable environment for her children. He then reset the hearing for 6 months later, giving her 6 months to "get it together". She continued to date, failed to find employment and had the attitude that the court was NOT going to tell her what to do. She lost custody, was ordered to pay child support, and given visatation. She was however able to continue dating and didn't have to get a job. Think about this carefully and decide where your priorities lie. You have much to lose.