*My sister has two children and back in the day they were very unruly, it was near impossible to get them to listen. They were only one year in age apart so they went through their " I don't want to listen" age together. My sister nearly lost hope with those two, because she was clueless as to what to do. She disliked yelling, like you, and didn't want to resort to a swift smack on their ass either.

*Then she discovered the art of rewarding them for good behavior. Whenever they did something helpful, or listened she gave them a reward. Not anything like a cookie, or food-like treat that would be gone in a matter of minutes and most likely forgotten; she either gave them praise, which made them glow just to be appreciated and treated like a big "boy/girl", or something small which they could play with and enjoy.

*My sister also took away something they held dear when they were being the worst. Like when my neice broke a plate off the dinner table my sister made her say "toot a loo" to her favorite doll for a day, it shocked little Megan into good behavior and she most certainly gained respect for dinnerware that day. My sister made sure to sternly explain why their bad deeds were indeed bad and/or dangerous, but never yelled. Her children tended to tune out yelling.

*I suggest trying this with your daughter, praise and appreciation for good deeds kicked the little devils out of my sister's children, maybe it will work with your daughter. Good luck