Hi
We miss detail as we will need the router model to be able to give some example if you want to do it the best way possible.
In big it's a site to site vpn you should look at.
That way when the client try to speak to the SQL server, which is on another LAN, the router route correctly the packet fort and back to that site without user intervention.
In example if your LAN where your PC are is 192.168.0.X, you could add the other LAN as 192.168.1.X, which the router will route correctly between the two site.
The public IP you have will make it easier to keep the tunnel up.