If you only had one standard glass of wine that day, and no other intoxicants in your body, then this case will likely either never be filed or will be dismissed in short order. The rest of this answer assumes you actually consumed more than one glass of alcohol.
Driving with a flat tire and driving too slowly are likely to be viewed by a court as vehicle code violations which would justify a police stop. Further, the police are generally allowed to stop vehicles while performing their “community caretaking” function, or to execute a “welfare check,” to determine if their further assistance or intervention is required. Your description indicates likely sufficient cause for the police stop, although one can always challenge this aspect of the case in a "fight all aspects of the case" kind of approach.
During these minimal intrusion stops, if the police encounter you behind the wheel, smelling of alcohol, or even just admitting to modest consumption, most courts today allow the police to investigate further, including initiating a DUI investigation. Therefore, the facts you offered do not immediately suggest a viable defense based on illegal police conduct, although it is important to confirm or dispel by carefully examining the police report and your written narrative of the events.
BUT: you may have substantial defenses in your case if your blood alcohol levels are confirmed low in the police report, and you did in fact perform very well in the field sobriety tests. In this event, you may very well have a triable case, arguing to a jury that your blood alcohol level was not .08 at the time of driving, and that you were not an impaired driver.
There also may be other defenses in your case, as with any other, with respect to legal procedure, science, or other facts or circumstances which come to light later.
The district attorney rarely dismisses charges that they have already decided to file against you. But yes, you can always fight a DUI. Whether or not you win depends on the strength of the evidence and the defenses. If you won, then you would be found “not guilty” or your charges would be dismissed. If you were to fight and lose, or alternatively obtain the best possible deal (for example, a reduced charge of “wet reckless” or better) then yes, you would have a misdemeanor criminal record, and also the DMV suspension consequences (don’t forget to call, or if you hire a lawyer, have your lawyer call, the DMV within 10 days of arrest to preserve your right to a DMV hearing to challenge any suspension; this information is contained on the front of the “pink temporary” that was likely handed to you at the time of arrest).
You should hire a competent local DUI defense lawyer to explore these and other issues with you, or, if you cannot afford a private attorney, then appear at your first court date and ask that the public defender be appointed to represent you. If you live in Sonoma County or you wish to browse more information about DUI’s, please feel free to visit my website at www.sonomacountyduilawyer.com.
Good luck
Jake