It is a mommy daughter dynamic that is out of your control. Don't take it too personally. My mother had a time with me growing up and it never ended. Thank God she never gave up on me and we are great friends now. That didn't start until I was probably 21 or so though.
One thing was mom insisted that I respect her and would not tolerate defiance, rudeness, or disrespectful tones. Time-outs didn't work for me....I would just play with my toes or something for as much as an hour at a very young age....So she had to resort to a spanking for the big issues mentioned above.
Most people would think that would make it worse, but it had exactly the opposite affect. She always did it in a way that did not humiliate me in front of others. She always talked to me about why I was going to be punished. Then she would follow up with another talk (even if I didn't understand it all) and explain that she loved me even when she was mad. That good or bad she always loved me and always would. I whisper in my girls ears everynight (even when we have had a bad day) that I love them always and forever...no matter what.
I respected my mother. I didn't always like her, but I always respected her and gave her the respect she deserved...even when I was a teenager. I can't say the same for my friends and those even included the ones that got along with their mothers. Many of my friends think their mothers are jokes to this day because they were never taught to respect them.
You can't beg, plead with, and try to manipulate your kids and expect them to respect you. They will see you as weak, vulnerable and push-overs...and they will treat you likewise.
Your little one is just testing her limits. She's battling your will. She wants to see what kind of resolve mommy has. Every child wants to be the boss...it's natural. Some are more determined than others. My oldest was easy. She tried but not very hard to assert her will...she's a big people pleaser and her defiant stages end quickly. My second child is much more head strong and her defiant times go for longer periods. She's always testing mommy's will out of the blue. (I blame it on her dad's genes.) :)
Just be patient, don't yell (save that for the very important moments when you need to get her attention...they become immune after awhile...I learned that from nine years in the classroom), be persistant, fair, and never give in (no matter how tired you are). You have to stick to your guns. Sometimes I tell my girls that they don't know who they are messing with and they won't meet a more determined (stubborn) mother. It gets a good laugh. But they know it's true.
You will make it. Just sit down and decide how you want to attack this. Make up your mind that you will not give up and decide that eventually it will work even if it doesn't appear to be working for a long time. She will come around if you are consistent in the punishment and methods you choose to use.
PS And she will sit in time out if you make her. You may need to waste lots of time standing over her...but if time-out is what you want to use, then stand over her and gently put her back on her bottom everytime she tries to get up. She will learn that you mean business and that she will do what you tell her to do. You will get tired, but she will come around.
PSS Make sure you have some time to unwind at the end of the day. It might be very stressful for the first week or so. If you like wine, you might need to go get a box for the fridge to sip at the end of the day. :)