Well mystery is solved 🙂
My first code above actually works:
<Style TargetType="{x:Type MyControls:ExtendedDataGrid}" BasedOn="{StaticResource {x:Type DataGrid}}">
<Setter Property="Template">
...
</Setter>
</Style>
I thought that it is not working becase VS (or Resharper) showed error in my code saying that resource is not found… Bug in VS (or Resharper) 🙁