WOW! Another story of a scuffle regarding a family sitting together in E+!
Check out
http://www.flyertalk.com/forum/showthread.php?t=469578 for a similar story.
The FA was not correct, DEN-OAK is not a short flight. Sitting in a middle seat for 2+ hours is not comfortable or an "even exchange". If anything I would have moved after the family asked, DEFINATELY not after the FA asked. She was wrong in that she didn't give her name and she definately played the wrong card, using security as an excuse

. She should have given you her name, regardless, United can probably look it by flight number and date. You should definately send a letter, although the crew probably prepared a defense note to her manager after the flight in preparation for your complaint.
I hope she is canned.