It sounds to me like you daughter is very smart, and that it may not be the case that she "doesn't want to learn", but rather that she doesn't want to learn what you want her to when you want her to the way that you want her to. That's not a bad thing, and that's not to say that you're doing anything wrong. But try changing your approach with her a little bit.
Instead of looking at flash cards for her to learn her letters, look at the "WalMart" sign on the building next time you're walking in there and ask her what the first letter is. Or make little "labels" for her things in her room and tape them up so she can see them (and you can read them to her as she's using that thing) every day, like "books", "crayons", "blocks", "doll", "door", "window", "wall", etc. To me it sounds like she is just active, and not interested in sitting down to learn things (like my daughter), so if you can get her to learn while she is being active, you may have more success.
Also, if she enjoys TV, let her watch "Seseme Street" every day. I try not to let my daughter watch too much TV, but she does watch that and I found that she knew certain letters before I ever taught them to her. When I asked her where she learned it, she said "Sesame Street."
And finally, if you have a computer, try getting some educational preschool games for her to play. My Mom and Dad used to each have their own computer, but when my Dad died she kept the newer one and gave the old one to my daughter, and bought her a few games. They have actually taught my daughter reading skills and math skills that I have never sat down and gone over with her. And my daughter has no idea she's learning, she just thinks she's playing a game.
And the final thought, on writing, instead of trying to sit her down and have her practice writing a certain letter over and over (I have yet to get mine to do that), ask her if she wants to write a note or card for Daddy or Grandma or someone else that's special to her. Ask her what she would like to write (like "I love you" or "Happy Birthday" or whatever), then write it (and her name) for her on one paper and ask her to copy it onto her "special card paper". Let her draw a picture on it or stick stickers on it, and then mail it (even if you're mailing it to your own address for Daddy). Kids get a kick out of the mail system and love to send and receive things, so this will be a fun game to her.
I hope these ideas help a little. Just remember that not all kids learn the same way, so just find moments throughout your day, even if it's only seconds at a time, to teach her the way that she learns.