First a "show cause" is essentially an allegation that you violated your probation on your DA and Poss of MJ charges. Even if you are not actively being supervised, you are still required to remain of "general good behavior" and not violate "any" laws. When you get convicted of a new charge (and in theory even charged), you are required to come before the court and "show cause" why either your suspended sentence should not be imposed or (which may be your case) a conviction should not be entered on the underlying charge. You should fight the drunk in public charge because: 1) it would be a basis for a show cause (even if the PO doesnt violate you, the CA or court can pursue one), 2) why not - its only punishable by a fine, and 3) you MAY have a defense.
To be convicted of the DIP, you must be "drunk" (or intoxicated) and "in public" (this is defined more precisely by case law, but could be your back yard if viewable by the public). You should get an attorney to review the case with you and go to trial if the CA is not willing to do anything. I'm not saying you have a winner, but you should certainly try.
Best of luck,
James S. Abrenio
This answer does not create a attorney/client relationship, but is intended solely in the court of discussion. It is always my recommendation to retain an attorney whenever a court appearance is necessary. This recommendation is highlighted when it relates to an individual's criminal record.
The DIP is only punishable by a fine, but a conviction could cause you to lose the benefit of the 1st offender opportunities in your other cases because it is technically a violation of your good behavior conditions.
You did the right thing by appealing the charge. You may have a triable case, and you should consult an attorney. You have nothing to lose by doing so, and lots to gain!