Did you try :
SELECT * FROM [LinkedServer].[RemoteDatabase].[User].[Table]
You need to specify your [] braces.
Also before doing that, you need to configure Lined server for the server database.
http://www.databasejournal.com/features/mssql/article.php/3691721/Setting-up-a-Linked-Server-for-a-Remote-SQL-Server-Instance.htm[
^]
Other than that, you can always have provision to do the same from your ADO.NET code.
Use
SqlCommand cmdServer1 = new SqlCommand("query", new SqlConnection("first server con string"));
SqlCommand cmdServer2 = new SqlCommand("query", new SqlConnection("Second server con string"));
By this way your application can separately connect to two server based on their respective connectionstrings.
Note : you should not copy / paste the code above, as I just showed you the code and there is chance for betterment.
:)