What is needed after my fiance arrives for her to Leave the country and re-enter the U.S.
I'm aware we can go through the advanced parole avenue but when will we be able to travel and re-enter freely ? Is it after we do her AOS?

There are only two ways to be able to travel outside the U.S. and re-enter.... that is AP, which is usually approved before the AOS, or after AOS approval, once you receive the GC.

You have to apply for AP along with AOS if you're going to go that route.

Good luck.