Two years old is too young to dress themselves. They don't have the coordination to be able to handle such a big job. At that age they are just experimenting on trying to put clothes on, but don't know how to do it yet.
This is what I did to dress my kids. When you wake them up in the morning, before they even really wake up, start dressing them. They will be half asleep still and just lay there as you dress them. By the time you're done dressing them, they will be woke up enough to get up and go to the breakfast table.
Wow- I just read your post that's amazing that she can dress herself, you have one smart cookie!