Well, since she is going to preschool in the fall I would continue with the gym NOW so she can get used to being away from you. Starting out at 20-30 minutes at a time will be a lot easier than jumping in with 1/2 a day.
ETA: Do you always give in to her because her tantrums are "fierce and you can't handle them"? If so you need to stop that now. It will only get worse.
This. So much this.
Unless your daughter has special needs that would make being separated from you an undue hardship, she needs more experience being away from you. I'd stick with the gym just for that reason alone. If its that severe now, she's going to have a hard time starting preschool.

