To force the control to forget which part had the focus you can change the DateFormat and then change it back again. So if it is set to dfShort set it to dfLong and then back to dfShort.
The trick is not to do this after the focus returns via the OnEnter event, but to do it before the focus is returned.
So the best place to do this is in the OnExit event.
procedure TForm1.DateTimePicker1Exit(Sender: TObject);
begin
DateTimePicker1.DateFormat := dfLong;
DateTimePicker1.DateFormat := dfShort;
end;