Change Entity connectionString at runtime error edmx (databasefirst)

Question

Was hoping maybe you could point me in the right direction as I seem to be at a block. I'd like to know how to implement this extension class? Where does usage code go? I'm using Prism and my DbContext is in another project.

edit

I changed my code to reflect that link below, I'm confused on the usage as it seems my code is not using the new generated connection string. When I put in a invalid server name, my application is still able to retrieve data. I should not be able to get data with a bad server name.

public static class ConnectionTools
{
    // all params are optional
    public static void ChangeDatabase(
        this DbContext source,
        string initialCatalog = "",
        string dataSource = @"",
        string userId = "",
        string password = "",
        bool integratedSecuity = true,
        string configConnectionStringName = "")
    /* this would be used if the
    *  connectionString name varied from 
    *  the base EF class name */
    {
        try
        {
            // use the const name if it's not null, otherwise
            // using the convention of connection string = EF contextname
            // grab the type name and we're done
            var configNameEf = string.IsNullOrEmpty(configConnectionStringName)
                ? source.GetType().Name
                : configConnectionStringName;

            // add a reference to System.Configuration
            var entityCnxStringBuilder = new EntityConnectionStringBuilder
                (System.Configuration.ConfigurationManager
                    .ConnectionStrings[configNameEf].ConnectionString);

            // init the sqlbuilder with the full EF connectionstring cargo
            var sqlCnxStringBuilder = new SqlConnectionStringBuilder
                (entityCnxStringBuilder.ProviderConnectionString);

            // only populate parameters with values if added
            if (!string.IsNullOrEmpty(initialCatalog))
                sqlCnxStringBuilder.InitialCatalog = initialCatalog;
            if (!string.IsNullOrEmpty(dataSource))
                sqlCnxStringBuilder.DataSource = dataSource;
            if (!string.IsNullOrEmpty(userId))
                sqlCnxStringBuilder.UserID = userId;
            if (!string.IsNullOrEmpty(password))
                sqlCnxStringBuilder.Password = password;

            // set the integrated security status
            sqlCnxStringBuilder.IntegratedSecurity = integratedSecuity;

            // now flip the properties that were changed
            source.Database.Connection.ConnectionString
                = sqlCnxStringBuilder.ConnectionString;
        }
        catch (Exception ex)
        {
            // set log item if required
        }
    }
}

Usage

    public void LogonClick(object sender, RoutedEventArgs e)
    {
      DialogResult = true;

      // assumes a connectionString name in .config of MyDbEntities
      var ADataEntities = new ADataEntities();
      // so only reference the changed properties
      // using the object parameters by name
      ADataEntities.ChangeDatabase
          (   
              initialCatalog: "",
              userId: "",
              password: "",
              // user Entered DataSource is the only change needed
              dataSource: (DataSource) 
          );

       Close();
     }

After the usage code above I verify the UserName in my DB and my DbContext is still using the original connection string in App.config.

  public void Authorize(string userName, string password)
    {

        var AuthContext = new ADataEntities();

        var query = from c in AuthContext.UserNames
                    where (c.UserID == userName && c.EmailAddress == password )
                   select c;
   {