It’s too bad your daughter didn’t communicate to you her assigned registration time. Any effort to register before is predictably fruitless, as you discovered. The times are assigned based on class and priority, with Echols, Rodman, and other scholars going first within each year. Many students will have enough credits to graduate early, so that threshhold alone would not give one first priority.
It sounds like your daughter had already communicated with the professor of at least one class, so I would be surprised if a follow-up email did not yield results.