As @RyanDev said, set up the database on the VPN as a Linked Server. There is an article on older versions here on CodeProject
How to Config Linked Servers in a Minute[
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Setting up a Linked Server for a Remote SQL Server Instance — DatabaseJournal.com[
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You've tagged the question with MySQL as well, so you may find this useful
Create a linked server to MySQL from SQL Server[
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It seems you can already log on to the VPN but for the linked server you may need to use a group logon or similar - you will need to discuss this with your network people who manage the servers. Check with them that there are no firewalls blocking any ports you might need. SQL server linked servers don't really care how the servers are connected (LAN vs VPN vs Cloud) as long as they can be accessed.