1. Once again, even if she is kind hearted, motus operandi would be to protect her offspring! Going back to the turtle duck thing, if I may, The turtle duck attacked Zuko for hurting her young. I, personally, see a much deeper meaning in this fact. The turtle ducks look harmless, but mess with their young and their on you. She only chided Zuko becaus eshe is most likely trying to teach him well. So yes, killing someone can be as easy as a motive, especially if the motive is protecting your favorite child.
2. I don't see how someone like Azulon would have a problem going back on their words. Royalty in our world is notoriously sneaky sometimes, how is this any different. Besides, as firelord, he can always say he never made any bargain. Your forgetting the power this man has. What he says goes. Dignity has nothing to do with this. Morality, perhaps, but not dignity. He sympathised with Iroh, I think, because he knew that a future heir to the throne, who had been groomed since birth for said job, was lost.
3. All sarcasm aside *cough cough* This part goes back to my previous point. Ursa was Zuko's only protector (Iroh aside) and if she could have done something else to save him, even if it meant going agaist her own morals, it would have been selfish for her not. Why let herself be killed while their was still a chance her son was still in danger? Who then would protect him?
4. Seeing as this is a more unadvanced society as the one we live in, poisons that we would be able to recognise with forensics, would not be detected. There are many plants that could do the job and such. It's not all as blatantly obvious as a knife in the back or something. Think back to our own past. Thik of how easily Kings were assasinated! With poisons!
5. It does explain other things. It explains my whole point. To sum it up: Ursa found out from Azula about what Azulon wanted to do to Zuko. Ursa went into "mad turlte duck" mode, and made the decision to kill Azulon, then she would have to leave, but she would at least know Zuko was safe (no threat from Ozai at this point). Then, Ozai probably helped to cover it up, because now there was nobody to say Azulon didn't make him the heir. Who was Iroh to argue?
So anyway, that's my idea. I know it wont convince you, but I'm sticking by it.