Allegedly Tried Fighting Cops in DUI Bust

The women who got arrested on a Delta flight on XMAS Eve after spitting on a passenger and striking him on the head, after grousing to a flight attendant that she was no Rosa Parks ... well, it's not her first run in with authorities, because we've learned she tried picking a fight with cops just a month earlier as she was arrested for DUI.

Law enforcement sources tell TMZ ... on November 10th, Patricia Cornwall crashed into a tree in Santa Rosa Beach. Sheriffs deputies arrived on scene and asked her if she needed medical help. She said she did not and was merely trying to get her car "unstuck."

According to the police report, Cornwall became belligerent, refusing to ID herself. She got out…