First, I give you a ton of credit. I stay at home with my daughter, and I know how long it takes to get ready to go to something simple like story time at the library, and there are no consequences for being late there. So, I can't imagine how frustrating it is to have to get your child ready and be somewhere on time where there are actual consequences for being late.
With that said, and this is NOT a judgement, but do you think your daughter is doing this so that she can spend a few more minutes in the morning with mommy? Could this just be her way of trying to get your attention? Again, please don't think I am judging that you go to work, I am just thinking of why it only occurs when you have to leave.
If it's not that, then it must be one of those wonderful phases that our children go through with no explanation as to why!!! Good Luck!