Hi Mariella,
I am a preschool teacher and run my own program. I've also been a nanny as well and know firsthand how difficult pick-up transitions may be. I read a lot of the posts below and agree that daycare is a big day for little ones. While it seems like fun and play to us, play is the work of children and it is work to follow along with the group and their transitions throughout the day. Your daughter's actions are a very age-appropriate response.
Tantrums at this age, in my experience (and this is supported by brain science), often stem from frustration or bodily need. Tiredness, hunger, and a need for some time to one's self are often the key reasons I see for tantrums in younger children. This is not the same as an older child pitching a fit for a toy, so you don't need to correct this. These tantrums are just her feelings, tiredness and frustration coming out. I usually try to circumvent the situations that can cause tantrums first, and then, if a tantrum erupts, try to give support ("I know you are sad/mad") with boundaries ("It's okay to be mad, and I need to make dinner. If you want to yell, you can do that in your room." or "I need you to be in here until you can be safe with your body". ) I have found that tired children often need us to just leave them alone to be angry, and they usually come out when they are ready for hugs and comforting. When this is done lovingly (as opposed to "Go to your room, I can't stand this!"), it usually gives the child permission to move through their emotions.
In my parent literature, I ask that parents be focused only on the children at pick-up time. The child is ready to reconnect with their parent and so phone conversations or conversations with other parents should be concluded before we say hello to our children. Not everyone will agree with this, but my colleagues and I have discussed this in particular, as we have noticed more accidents and tears when parents linger to chat with each other than if they just pick their child up and leave at once.
Our children want to connect, so be available for them. I also ask that parents have a healthy snack ready in the car as well. There's nothing worse than driving home with an upset child who's hungry. Children get busy with playing and may not eat enough at daycare or preschool. And I suggest some unstructured playtime in their own space once they are home. This might be a place off the kitchen while you are cooking dinner, or some playdough to pound at the table. Many children are all done with taking turns and sharing by this time of day, so if you have multiples, consider trying to find each child a little space of their own.
Most importantly, I like to remind our families that tears at pickup really don't have much to do with us, their parents. I see older children who are upset at pick-up sometimes, too. When I was first nannying, I'd be hurt to see a child burst into tears at the sight of me when I was picking them up. As I matured, I realized that this is ALL about them and had nothing to do with me.
And yes, early bedtimes are definitely recommended.
If you have more difficulty with the transition while *at* the school, see if you can get your daughter's caregivers on board. In some cases, perhaps you can call the classroom when you are about 10 minutes away and let the teachers help your daughter transition out of playing and into her shoes and coat. I once led a toddler classroom where we actually handed a child out the door and into the hallway to their parent instead of having the parent come in to dress and ready the child for leaving. This helped her family immensely. Positive changes like these can sometimes help. Good luck!