Why do you think Shakespeare includes a scene showing the relationship between Lady Macduff and her son?

Answer 1

To increase our sympathy for her and to make us dislike Macbeth even more when he has them killed. It was dangerous to portray the overthrow of a monarch by force because the government might take that to be encouragement to assassinate the King or Queen (and people tried to kill both Queen Elizabeth and King James, so this was a real fear.) Therefore in order to show the overthrow of a king to be justified, the king needed to be shown as an absolute monster. What better way to do this than by having him kill an innocent woman and her spunky kid? Especially the kid. Killing babies was then as now an especially horrifying thought.

Answer 2

The audience is likely to react to the killing of a child and an innocent woman, but much more strongly if we meet the child and the woman first. Macduff had other children who were murdered, but nobody thinks about them, because we never see them. The scene causes us to feel the anger, Horror and deep sorrow that Macduff feels, so we can sympathize with him later when he chops off Macbeth's head. In order to dramatically and politically justify the killing of a king, that king has to be portrayed as a monster (see also Shakespeare's Richard III, which has almost the same plot.)