What happens if I am on probation for shoplifting charged with a misdemeanor, and get charged with a minor in possession of alcohol, misdemeanor, in another city?

Probably just more restrictions,odds are the court system your dealing with in the other city for shoplifting won't even know about it,but for the alcohol you may get drug tested by that court system,alcohol really isn't as big a deal though,your pry fine,you may want to ask a lawyers opinion,I'm on probation for 3 misdemeanors myself,just keep your **** straight and stay out of trouble dude

Well first if you don't tell your PO, and they find out when they run a normal criminal history on you, you will be revoked for sure since failure to report is a serious violation.

Reporting any police contact is a requirement of probation.
So Dusty gave you some very poor advice about trying to hide it.

It will depend on the judge where you are on probation, most likely a warning and put back on probation, and you will be on probation in two different areas.