Parking at UF is a PIA no matter whether you’re student, faculty, or staff. I don’t know much about how the ZipCars work or how convenient they are-- but perhaps the best option would be to have her go car-free for a semester or two and see how it works out.
Be aware also that the bus system is free for anyone with a Gator One card. That can get her to the mall, downtown, and many other places. (info at go-rts.com ) The buses are clean, safe, and air-conditioned. They do not always run as frequently as one might wish, but they are an option.