Thanks you all for help, your clues was very helpfull.

Here is some code that works for me when it comes to construction connection string but I have tested it only on localhost.

SqlConnection cn = new SqlConnection(ConfigurationManager.ConnectionStrings["SiteSQLServer"].ConnectionString);
            string serverName = cn.DataSource;
            cn.Open();
            string providerName = "System.Data.SqlClient";
            string databaseName = cn.Database;
            cn.Close();
            SqlConnectionStringBuilder sqlBuilder = new SqlConnectionStringBuilder();
            sqlBuilder.DataSource = serverName;
            sqlBuilder.InitialCatalog = databaseName;
            sqlBuilder.IntegratedSecurity = true;
            sqlBuilder.UserInstance = true;
            string providerString = sqlBuilder.ToString();
            EntityConnectionStringBuilder entityBuilder = new EntityConnectionStringBuilder();
            entityBuilder.Provider = providerName;
            entityBuilder.ProviderConnectionString = providerString;
            entityBuilder.Metadata = @"res://*";
            string myConn = entityBuilder.ToString();
            EntityConnection myConnection = new EntityConnection(myConn);