Difference between Have a laugh at someone and Have the laugh of someone

have a laugh at someone—find smb. amusing; ridicule a person:

• You let them in to have a laugh at them or you let them in because you want to listen to what they’re saying.

have the laugh of someone—turn the laugh against smb.:

• “Why, he always used to laugh at you as the dunce of the family!” “I know, and now I shall have the laugh of him, shan’t I?”