Very interesting question, however I would focus a question like this on how Bronte uses repetition in the novel rather than fate as a separate force. If you compare fate in, for example, a play like Romeo and Juliet, it is clear that fate is a major force that wills the destruction of the lovers. The characters are the playthings of fate and the ending is inevitable. However, Wuthering Heights cannot be described like that. Instead of fate as a force, Bronte seems to use repetition of various themes and topics through the generations. This is a key aspect of Gothic literature, which focuses on how issues or curses effect not just the first generation, but go on to haunt second and third generations.
Taking this view we have plenty of examples of how this repetition occurs. For example, Heathcliff is oppressed by Hindley as a child. Heathcliff gains his revenge by oppressing Hareton. Consider too how the younger Catherine´s mocking of Joseph eerily echoes the same taunts of her mother. The world Bronte paints is one where the characters don´t seem to be able to shake off the influence of their ancestors, and the repetition of names in the novel forces us as readers to consider how plot elements endlessly repeat themselves, and characters seem to be scrambled up versions of their predecessors.
So I am not too sure that fate is the right word - the characters seem caught up in plot events that eerily echo what has gone before, but at the end with the death of Heathcliff that characters seem free to break away from this repetition and start a newer, happier life, symbolised by the union of Hareton and the younger Catherine.