Can I restore database A to database B but keep B's permissions? I have a live db A and a test db B. The live db is backup'd every day. And I use A's backup file to restore to B to keep in sync. But then B's permission setup is also overwritten by A's. Can I only restore A's data but keep B's permission?
A SQL Server database backup is the whole database, users included.  You can script out the permissions prior and reapply them as part of your process while blowing out the other permissions.  You could make your db schema work on both environments.  You could also just do data exports and load up data.  Tools like RedGate Data Compare could also help keep the data in sync.  

If you want to give more info about your environment we can help guide you to the best option but you have several.