In case you don’t have full access to SQL Server and the machine that is running it you can’t really initiate a restore command (maybe there are some workarounds but I’m not familiar with any).
What you can do if SQL Server is on a public IP address is setup some kind of replication between two servers so they synchronize automatically. Again, not sure if this is possible w/o full access to machine but you can give it a try.
Final solution would be to use one of the third party comparison and synchronization tools to synchronize databases at a given time. Just find a tool that has command line interface such as Data Diff from Apex. Another one you can use is Data Compare from Red Gate but I’m sure there must be others too.
Note that these tools are not free …