It sounds like you may be unintentionally reinforcing this behavior in your daughter. Also, check your expectations of her behavior. If you expect resistance, you are likely going to get resistance. Kids are wonderful readers of our body language and moods and will mirror them in response! She doesn't "make" Mommy mad. Nobody is in control of another's emotional responses. It is likely you feel rushed to get to work on time and thus may be responding to her impatiently. This creates a cycle of her responding to you in a negative manner, which in turn probably doesn't alleviate your feeling of impatience and increasing level of frustration with the situation.
It may be helpful to lay out her clothes for her the night before. Help her get dressed in your room alongside you while you are getting dressed so you can help her when she gets stuck...remember, she is still trying to learn to master such self-care and should not be treated as if she was born knowing how to dress herself as an older child would.
Set your alarm 15-30 minutes early to give you and she time to get ready without feeling rushed, and thus without increasing negative feelings mounting as a result. You will also need to go to bed earlier to ensure everyone (you included) are rested so that nerves aren't easily rattled.
Also, check yourself in how you are modeling handling your own level of frustration through monitoring your tone of voice, volume of voice, body language, and how you speak to your daughter. If you speak disrespectfully to her because you are angry, you will most definitely get that in return!
Some kids whine, so don't pay any attention to it. Just interact with your daughter as if she isn't whining and that should eventually stop.
In addition, make sure you are following through on what you say you are going to do and that when you discipline your daughter (this is a different concept than punishing), you are giving consequences to her behavior that are logical and apply to whatever rule she is breaking at the moment.
It might be helpful to consult with a professional therapist to help you learn to change your behavior so that your daughter's changes also as a result.
Good luck!
Sincerely,
S. M. Wolf, M.A., MFT