The feud between Macbeth and Macduff is directly proportional to the premonition of the three witches at the beginning of the play. Macbeth had an obsession with one specific prediction in which a certain line of princess would take his crown. However, these princes were not of his own bloodline, for which he had to make them disappear.
Macduff had slowly uncovered Macbeth's true persona and weaknesses for which he professed (and switched) his loyalty to Malcolm. When Macbeth realizes that he has lost the loyalty of Macduff he sends for his family to get killed. Later on in the play he realizes that Macduff was part of the prophecy: Macduff was not born of a natural mother, and his anger against Macbeth will eventually lead to murder, hence, another prophecy will be fulfilled.
Macbeth's decision to murder Macduff's family seems to have been made in extreme fear and haste. None of the murders which Macbeth commits can really be justified; however, at least one could argue that King Duncan and Banquo posed direct threats to Macbeth's position. But Macduff does not, and Macbeth fears that somehow Macduff will stand in the way. Macbeth has been driven anxious by the witches' prophecy. This suggests that the influence of the supernatural has taken a serious hold on Macbeth. He has interpreted the prophecy in a way that appeases his own inner ambition and greed and uses it as justification for committing evil deeds.
In Shakespeare's Macbeth, the supernatural, the weird sisters, give Macbeth mixed messages in their predictions of Act 4.1. Thus, the responsibility for Macduff's family's murder lies with Macbeth, much more than it lies with the supernatural.
While the witches do tell Macbeth to beware of Macduff, they also tell him that he cannot be harmed by anyone born of woman, and that he cannot be defeated until Birnam Wood comes marching toward his castle. Macbeth makes his choice to emphasize one prediction or warning over the others.
Thus, Macbeth is responsible for his own decision to order the slaughter of Macduff's family. If the witches only tell him to beware of Macduff, period, then you might be able to argue that the supernatural trick Macbeth into taking action against Macduff. But they, in fact, tell him to figuratively laugh at anyone who would fight against him. They tell him not to worry.
Yet, he still goes ahead and orders the slaughter. He can't get to Macduff, so he gets to his family instead. The slaughter serves no political purpose, and no motivation for it is given in the play, except that Macbeth acts impetuously and immaturely and orders it.
The only link to the supernatural in the decision to kill Macduff's family, is the warning Macbeth gets from the witches to beware Macduff.
Since he cannot physically get at Macduff who has fled to England, Macbeth does what he believes to be the next best thing, he kills the Macduff family.
Macbeth figures that this action will destroy Macduff's will to fight. It is a calculated risk that Macbeth looses. Instead of destroying Macduff's will to fight, the murder of his wife and children gives him added incentive to kill the tyrant.