I want my Sim to get her degree as soon as possible. My sim is only on her second day of Uni but I would like to know if once she gets home, does she have to wait before she re-enrolls or can she re-enroll right away?

You can enroll as soon as you get home no waiting period

Okay. thank you.

All you have to do is re-enroll to go back to school. The time between semesters is up to you. You get home on a Saturday usually and can leave again on Sunday. There is no waiting period unless you want to take some time off to do things in the home world. If you don't re-enroll by Sunday then you have to wait a week it appears to go back the next week. I usually do 2 semesters at a time (you can enroll for one or two) - you don't go home between those two but don't go to classes on the weekend - saves re-enrolling as much as you have to if you pick one at a time