Are her feet close enough to the peddles of a tricyle so that she doesn't have to reach to firmly place her feet on the peddles? Some peddling toys do not have adjustable seats and when my grandson first wanted to peddle he could just barely reach the peddles so he could not get enough force going forward.
If that's not the problem, try holding her feet and pushing forward for her.
Before she becomes upset distract her into doing something else. By not being able to do this to the point that she's to the point of a tantrum she most likely is convinced that she cannot do it. when we fail over and over we have a tendency to quit trying different ways of doing something. Our emotions are too strong to learn and we expect failure. It's a good sign she keeps trying but I think it's time for the adults to intervene and take the pressure to succeed off her.
Perhaps you or the day care staff could find something else for her to do in which she would be successful and that she would want to learn.
Children mature in different ways and it's possible that her body doesn't have the ability to ride a trike at this time. My grandson is 4 and he still doesn't ride a trike. At daycare he rides the toys which have no pedals. He can push with his feet.