Unlawful detainment, arrest??

Prince William County, Virginia. I was a passenger in a vehicle stopped for suspicion of DWI. Driver was tested, handcuffed and placed in police vehicle. Officer came to passenger door and asked if I had been drinking. I replied yes. Officer told me to step out of the vehicle. I complied. Officer performed a pat-down search, removed items found and placed them back in the vehicle. Officer told me to face vehicle and placed hands behind my back. I complied. Officer handcuffed me and advised me I was being arrested for "Public Intoxication". I was then transported to a police station, along with the driver, where I was cuffed to a bench while the driver was processed for DWI. I was simply asked for name and address at police station. I complied. We were then transported to a detention facility, where we were booked and placed in a cell. I was released 8 hours later and given an option of paying a $53 fine by mail or appear in court for violation of the "Public Intoxication" law. My question is, was this arrest and subsequent detainment legal? The Virginia code reads that arrest and involuntary detainment in this case is not, but it's not very clear in the law, just a brief statement. Also, does it appear that I may have been coerced into being in "public", as I was inside the car and not in public, but only became that way once the officer ordered me out of the vehicle. The police were very mean and intimidating, even though I was cooperative. I also was never tested for BAC, does that have any bearing? Thanks.