Bert, I am not sure I understand the need to use LogMeIn with an Application that runs SQL Server.

SQL Server is an IP Addressable Database, as such the connection string, whether it is ODBC or .Net will include all of the info necessary for the Application to connect to the database.

If you are using VPN you should be fine because you will be "in your subnet" and the SQL Server should be found automatically.

Outside of your firewall, remember SQL Server listens on Port 1433.

"The illiterate of the 21st century will not be those who cannot read and write, but those who cannot learn, unlearn, and relearn." ~ Alvin Toffler