I've been there! Having a routine is helpful. My son wakes up, has milk and watches a short cartoon. Right after that he sits down to breakfast and then uses the potty and gets dressed. He's pretty good about putting on what I give him but if he has trouble, he gets two choices. I'll say something like, "you can wear the shirt with cars or the shirt with stripes." Giving him choices helps and makes him feel like he's in charge...just keep it to two. If he can't choose then I choose for him. If he can't get dressed, then I dress him kicking and flailing - when this happens it is because he is overtired, hungry or anxious about something.
I also talk him through the routines a lot, first thing in the morning when he wakes up I'll say "First we are going to have milk and watch one cartoon. Then, we eat breakfast and get dressed! Then, we go to preschool!" I have found sticker charts to be a helpful motivation in the past - ex. she gets to put a sticker on her chart if she gets dressed. After so many, she gets a treat. I have used these when I've had trouble with my child following a routine, you can find free charts online.
It may also very well be that she's a bit anxious about the new teacher at school. That could be the reason for the tantrums and is very normal. You say she is fine when you pick her up, so it's probably okay. I would ask the teachers for suggestions on how to deal with it, they've seen it all and are very good at offering advice most of the time.