As already suggested you can store two different connection strings and then you can open two separate SqlConnection objects, on per each database.
However, to give you an alternative, you can also define a linked server in either of the Sql Server instances. Using linked server you can achieve a situation where you connect only to one database server which then again connects to another. This way you would need to have only one connection in your application.
To query the data 'behind' the linked server you need to use special four-part notation for tables. If this feels cumbersome you can always define a view to hide the location of a table.
More about linked servers: Linked Servers