yeah, but just because you aren't blood doesn't mean you aren't family. and yeah, if she had a surge of adrenaline, she would probably kill azulon if he was charging at zuko with a knife, but he was only planning on killing zuko. it wasn't going to happen for at least a day or two. she had time to think. azula would have been the first to spill the beans on the whole situation, and then ursa would have gone to other people (ozai,??the executioner, etc.) to see if??azula was right or if this was her twisted idea of a joke. she would have had time to digest it a little bit. there wouldn't have been any adrenaline.
nd a traveler's cloak proves nothing. i disagree about the wedding gown thing, but maybe she was wearing the cloak because.... i don't know, maybe the sun was just starting to come up and she didn't want anyone to see her heading down to be executed. i wouldn't want anyone to see my face. if i was going to die, i would want as little people as possible gawking at me, trying to figure out why a princess was heading down to the executioner's. she could just be hiding her face. just because it was a traveling cloak, doesn't mean she was about to travel.
and also, in the episode (you'll probably think i'm reading too much into this, but i think it's relevant) when ursa is in zuko's room and telling him "never forget who you are, blah blah blah, everything i've done to protect you, blah blah blah" and then we hear footsteps coming from the hall. "they were coming after her" you say? "they were looking for azulon's killer" you say? the footsteps were walking. pretty slowly.if they were coming to catch her, someone would have been running. but if they were coming to collect a prisoner from a room, who wanted to say a few words to her son before she died ( ) then they wouldn't have been running.