Jeepers it is very normal for a child to have difficulty adjusting to any sort of change, especially without warning. When you take her to nursery she has a routine to follow and lots of cues to help her prepare for leaving you, eg getting shoes on, leaving house, getting in car, etc. She can follow the routine and begin to predict what is going to happen next.
However while she is at nursery she has no idea of the time and no cues to follow for your arrival. You suddenly appear to take her away, without warning she has to finish her enjoyable activities and leave. The abrupt change is hard for her to take in and so she reacts badly.
Do you arrive each day at a set time? Could the staff spend some time with dd each day getting her ready to go home, for instance sing a good bye song, start to get coat on etc, before you arrive? I would explain that you are getting very upset by the unhappy reaction each day and that anything they can do to help her with the transition from nursery to home would be appreciated.
The other thing to consider is that attached children reserve their worst and most negative behaviour for the adult with whom they feel most secure. Your daughter probably doesn't feel entirely 100% secure with the nursery staff and so to some extent is putting on her best behaviour for them. When Mummy arrives it is time to open the floodgates and let out all the stresses of the day in a whoosh of emotion.
I don't know if either of these explanations ring true with you but I have seen them both in childcare situations and in my own experience as a nanny. I am sorry you are being so hard on yoursel - your dd sounds like a confident and secure little person to me.