Maybe just explain to her that you understand she may be busy, however, you are trying to accommodate a start date for her in mid September and in order to do that you need to hear from her by such and such a date; otherwise, she'll have to start in October as originally planned.

Try to take things with a grain of salt on here. You sound stressed and defensive. Take a deep breath, you'll work it out. We have to be more patient with some parents than others. I'm sure once she starts daycare it won't be so hard to communicate with her.