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DearCustomer- If there was no other offenses related to the incident then it should be a misdemeanor. I know of no public consumption statute that is a felony unless it would be related to another crime such as violence. Assuming this was just an open container violation it will be a misdemeanor.
You certainly have a right to plead not guilty and contest the charge. Most of these ordinances are designed to prohibit drinking outside of the licensed establishments and are basically used to harass persons like you. The offense is a minor one yet it will appear on your record if you are convicted or plead guilty. I know these "programs" are a pain and what they really are is a way for the city to make money.
If she can do the program that will keep her record clean but if not the simplest thing to do is to pay the fine. The record can likely be expunged in the future if she receives no other violations.
Well a no contest plea really is the same as guilty so that isn't going to matter. It would be up to the court whether they would now accept her into the program since she declined. I can't answer for the individual judge in a specific case. She would have to contact the court and tell them she would like to enter the program and see if something can be arranged.