I'm glad you enjoyed it. Lucius would've probably liked to take Draco somewhere more private, I agree with you there, but it was clear that Draco would not consent to go anywhere with him (except perhaps by force which Lucius didn't want to do). So he really had no choice but to confront his son right then and there. Also I think the shock and anger that he felt due to Draco's disobedience overrode his judgment as well. Anger can blind men quite thoroughly after all.

But of course, to each his own and all that jazz...