Why does the DataGrid not update when the ItemsSource is changed?

The ItemsSource is always the same, a reference to your collection, no change, no update. You could null it out before:

dgOrderDetail.ItemsSource = null;
dgOrderDetail.ItemsSource = OrderDetailObjects;

Alternatively you could also just refresh the Items:

dgOrderDetail.ItemsSource = OrderDetailObjects; //Preferably do this somewhere else, not in the add method.
dgOrderDetail.Items.Refresh();

I do not think you actually want to call UpdateLayout there…

(Refusing to use an ObservableCollection is not quite a good idea)