In Macbeth, (II.iv), is there a purpose to murdering Macduff's son dramatically on stage & not showing the murder of Lady Macduff?
I would expect that this question is based upon opinion. My opinion is as follows.
In Shakespeare's Macbeth, I would assume that the murdering of Macduff's son (who is called "Son"—"Egg" is a nickname by the murderer) is not something that would upset an Elizabethan audience as much as the murder of a woman. (By comparison, today's audience would be upset at the death of both.) A young boy would have—not too long before this—been a squire to a knight at a young age. Squires did not fight, but served their lord in battle, which did not guarantee their safety. The idea of women fighting was an Anglo-Saxon concept, not an Elizabethan one. (However, Joan of Arc would have been the most recent example of a woman fighting, around 1431—not that long before the play was written.)
In my opinion, the fact that the boy tries to stop the murderers shows that he is valiant at a young age, Macduff's son completely. This, and Young Siward's death on the battlefield, would have vividly shown the depth to which Macbeth has fallen since killing Duncan—he now casually takes the lives of women and children. The boy's death would have upset the audience but they would have been gratified by his willingness to defend his mother and family. The murder of Lady Macduff off-stage would have less offended the audience than watching it acted out before them.
Shakespeare wanted to establish that Macbeth had ordered the murder of Macduff's entire family. When Macduff hears the bad news in England in Act IV, Scene 3, he asks:
All my pretty ones?
Did you say all? O hell-kite! All?
What, all my pretty chickens and their dam
At one fell swoop?
Shakespeare could not show the soldiers murdering all of Macduff's children, so the one boy who is murdered onstage has to symbolize all the others. It is this outrage that motivates Macduff to seek out Macbeth on the battlefield and kill him in their climactic death-duel. The murder of Macduff's wife onstage would not have seemed so terrible as the murders of perhaps as many as half a dozen of his children. His whole line is cut off "at one fell swoop." He is all alone in the world. Macbeth intended to teach Macduff a lesson for deserting his cause, and also to use the atrocity as an object lesson to dissuade other thanes from following Macduff's example.