If I had done this as a child, my mother would have grounded me and taken away the tablet. Showing your parents disrespect and telling them to "shut up" is most certainly not OK. You need to convey this to your daughter, lest the problem grows out of hand. It is not necessarily the amount of screen time that is the problem, as long as she is finishing her work, but rather her attitude towards you.
Do you remember long, long, LONG phone conversations with friends in your preteen and teen years? I certainly remember talking to my best friend for an hour at a time, tying up the family phone. (Sounds kind of quaint, doesn't it? My friend's mom put in a separate line for her kids.)
If your daughter is doing her homework and keeping up with her after-school activities, I'd stop saying no on the screen-time thing and just sit down and work out with her what a reasonable schedule is. You could even pencil it out. Tell her you want this particular hour for the family, this particular time for her to prep for bed, and she can have this particular one for texting with friends.
I think you see this as a cause of her turning away from the family in some way. Guess what, it is the job of a teenager to turn away, in preparation for standing on her own two feet as a capable and autonomous adult. The texting is not a cause of this. It's just a symptom. She will grow up and away, whether or not you prohibit her to be online. I'm sorry, momma. But she will still love you and still be your child, all your life, don't worry. She is growing, you need to do some adapting. Time does not stand still.
She is constantly on social media communicating with her friends or playing video games. She does it after she finishes all her homework or comes home from her activities, sports. I feel it is excessive. But this seems like the new way kids are communicating. She doesn't even have a phone. She uses our family tablet. How much is too much? How can we control this? She is also being extremely rude. She tells me to shut up when I say NO to her. We really have worked hard to raise a kind and caring daughter. She had changed so much this year since her and her friends are using tech devices. We are a close knit family. I am very frustrated by all this. It's affecting our home life
What do you mean by "screen time"? Is she texting and on facebook or twitter, communicating positively with her real-life friends?
What does "she reads a lot, so it doesn't get in the way of her work" mean?