Hi Emily,
I feel your fustration. Kids can just drive us crazy!
One thing is, cut way, way back on tv/computer time. Especially broadcast cable TV. I REALLY see a difference in my kids when they have tv time. (and I don't have cable, just videos to watch) I would edit all movie watching to only G rated, and even then, be particular. The movies of the day love to portray broken families and especially sassy kids with no respect for authority or anyone else. These are bad examples and we don't want our kids to role model it.
When you talk to your child, gently hold her shoulder and bend down so that you are eye to eye. Be right in her face. Give your instruction once, in a very calm and nice but authoritative way. Be polite. Ask her to repeat it back to you.
If she disobeys the instruction, YOU KNOW FOR SURE she heard you and she has disobeyed. This is now where punishment for disobedience must happen EVERY time. WHen you know the child will pay for the crime, there is no need to be angry. You may even feel pity. But be loving in your discipline and mostly be consistent. You are trying to break a habit that she has been allowed to develop. It's going to be hard but hang in there.You are building character that will stay with her the rest of her life.
Even if my kids say they forgot, they still get punished. Why? Because there should be no excuses for disobedience. (Unless they were physically restrained from following directions.) Someday they will have a supervisor, and saying "I forgot to do my job" won't stop them from being punished (fired !)
Robert Shuller once said "Tell them they are , what you want them to become." I use this strategy a lot and it WORKS! It works where in contrast belittling our child's failures doesn't work. Kids generally do want to please us, they long to be patted on the back. A habit we parents get into is telling the child of all the bad habits he/she has. But if you can catch your child doing something good, and truly complement it, watch those children bloom! and even become what you are suggesting. For example, I told my son after he picked up a penny a handed it to his sister, "God gave you the gift of a giving heart!" Boy, after that he really filled that role. He's always thinking of what he can give others. To my youngest I said" wow, you are a great cleaner! I have never seen another child who can clean as well as you at your age" She has lived up to that suggestion! To my oldest I said" I think it's neat how the little kids look up to you. I bet it's because you really get down to their level and talk about things that interest them." She is the pied piper of the little kids now and has found she truly does love them.
Lastly, don't underestimate the power of God to work in your family. Pray out loud for your family, ESPECIALLY after you punish them or after a fight. Pray with your daughter. and with her listening... ask for God to give your daughter a heart that "sees M.'s pain and M.'s desire to be close again..M.'s desire to grow in love and forgivness...and Lord help my daughter forgive me for my shortcomings, and lord, help me forgive my daughter." The Lord has the power to change your household by changing you first. He can do that only when you have asked him to come into your heart and live there (he is a gentleman and won't come live with you unless you ask.)Once he resides there he can work on you, and in turn , your whole family. It works. try it. The bible says "taste, and see that the Lord is good"
You are going to have to rebuild your relationship with daughter. You may both disrepsect eachother and many times may not like eachother. Both of you probably harbor resentment. Until these emotions are dealt with and forgiven, you will not move into the loving relationship you are desiring with her. Everything you need to know about how to relate to others is in the Bible. I've read a LOT of help books,in fact several of the family self help books listed herein by others. They all have their great points, but you still have to deal with anger and resentment. That emotion/sin is from satan and he wants to see your family fail. The Bible has laid out every step to defeat the sin of satan. Read it, LIVE IT, and it will change your life. Read, Proverbs, Ephesians, Romans, 1 Corinthians, Phillipians, Luke, John, Peter and James.
"Train a child in the way he should go (in righteousness), and when he is old he will not turn from it" Proverbs 22;6
"All your sons will be taught by the lord, and great will be your children's peace" Isaiah 54:13
"A wife of noble (God fearing)character who can find? She is worth far more than rubies...Her children arise and call her blessed; her husband also, and he praises her"
Proverbs 31:10, 28