Can I reverse a plea deal on a DUI if the Public Defender wrongly advised me to take it.

I got a ticket for running a stop sign, speeding, open container of beer in car and arrested for dui. Public defender said take the deal for dui because there was no jail time in the deal. I beat the other charges because the cop lost site of the car during pursuit and could not say for sure that i was driving the car the he originally saw. I was not even in the car when he saw me, the beer was not in the car and the keys were not in the car. Now that means that the cop can't even prove that I was driving that night, but just that he saw me outside my car having a beer on my own property. The cops narrative even says that he lost sight of the vehicle for a short time during the pursuit. If he can't prove that I was even driving or that my car was the one that he saw run the stop sign then I think he can't prove the dui. The public defender said that the pursuit leading up to the arrest had no bearing on the dui charge.