I'm not sure that this is an SQL Server question, since your problem seems to be with running IIS. But if they are connecting to SQL Server through a web browser and IIS, they must have been logged into your Windows domain before they open the browser. Runas on the web browser could work.

But it seems to me that a better solution is that they log into a terminal server on your domain, or that you provide virtual machines joined to your domain. In the latter case, you could put the VPN connection on the VMs.