Michael Parker's (Daniel Ings) divorce was portrayed by the press as a scandal and eventually he resigned. He later said that the Duke was supportive and "the Queen was wonderful throughout. She regarded divorce as a sadness, not a hanging offence." In a public show of support, the Queen created Parker a Commander of the Royal Victorian Order (CVO).
The poem recited during Prince Philip's investiture is 'Ode on the Death of the Duke of Wellington' by Alfred, Lord Tennyson.
The episode makes it sound as if Philip's request is somehow unreasonable and that he somehow wants to usurp his son. But Philip was born a Prince and was forced to give up that title when he married Elizabeth. As has been pointed out elsewhere, when Victoria married Albert, Albert wasn't forced to give up his Princely title.