How familiar are you with powershell or even command line programing as this can be easily achieved by creating either a powershell script and utilising the sql server modules or via a batch file using sqlcmd.

It would require your SQL server agent to be setup as an account that has the necessary privilages to run the required backup \ restore against the SQL servers and access the files that are written to and read from.

You would then have a SQL agent job that called the .bat or .ps1 script and this can be executed on demand or at scheduled times.