Reuters posted an article on October 2 about Goro Miyazaki's struggles to overcome his father's shadow. It's a good article, that covers Goro's career and the considerable tension between father and son. Bonus points for quoting from the son's production diary (one entry was titled, "Zero Points as Father, Top Points as Director") in the article.
The tension between father Miyazaki and son has been written about throughout the production of Gedo Senki. I remember Goro mentioning in another article that he and his father hadn't spoken to one another for over a year. Messages between the two have been passed along by third parties, old friends like Toshio Suzuki and Michiyo Yasuda.
Anyway, be sure to read the article if you haven't yet done so.