Test Two SQL Connection Strings to work over MPLS

Hi All!
I have a small program that connects to our local SQL server to pull a small amount of data into a Windows Form.
We have an MPLS connection with our parent office and I need them to be able to connect to the SQL server as well using the same code. I am wondering how I would go about testing the SQL Connection string to work in both locations.  E.g. if the first connection string is not valid then use the second connection string.
We are on two different domains, so it becomes a little more difficult.  But I have tested both connection strings individually and they both work.
This first connection string is what I use on our local network:
Dim connString As String = "Data Source=SERVER\SQLEXPRESS;Initial Catalog=DATABASENAME;User ID=USER;Password=PASSWORD" This next one is the one I use from inside of the parent office over the MPLS. Note the addition of the Domai ...