CickOnce Application authentication problem outside domain over vpn

[forumlrnmr]

I have a ClickOnce application which uses Windows Authentication that I've installed on a workstation. This application was developed on site at a client and the installation and database configurations are all internal to their domain. We have the need to create a "stand-alone" installation that can be installed on a machine off the client's domain that will work once we connect to their VPN solution. I've tried to create a stand-alone installation however the code still references a database connection string that I believe is the problem that is keeping this application from working remotely on VPN.

How can we pass SQL database connection strings correctly with the full domain name?

What other ways might I approach sending any authentication coded into the application over a VPN?

Thank you in advance for any assistance!