Remote Database is strictly not allowed in Shared Hosting Servers.
You can use the following connection sting for connecting to MS SQL Server 2012 database
Connection to a SQL Server instance
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<add key="ConnectionString" value="Data Source=.\MSSQLSERVER2012;Initial Catalog=database_name;User ID=db_user_name;Password=db_password;Persist Security Info=True;" />
Connect to SQL server via TCP/IP Protocol
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<add key="ConnectionString" value="Data Source=localhost,1437;Network Library=DBMSSOCN;Initial Catalog=database_name;User ID=db_user_name;Password=db_password;Persist Security Info=True;" />