I grew up with dogs, so i know what your talking about.
First, what is the definition of "storm" are you using? is it when there is massive thunder and lightning? or is it just a little rain?
If you truly do not wish to return her to the rescue center, then go with the medicine. Think about it, how often is there a storm? not that often. Sure, you can have a week where it storms for 4 days out of 7, but that passes. Majority of the year are cloudy to sunny days. Thunderstorms rarely happen, So if i was you, id stick with giving the dog the medicine to help keep her calm. By the time she comes out of the zombie stance, the storm is over and your dog is happy.