But both Andrew and his ex-wife Sarah Ferguson did "not attend the shoot itself", however, the former couple did drive down to join the shooting party for a meal at the York Club.
"It seems quite brazen of Andrew to host a party and let his family go shooting with all the controversy raging."
The party was reportedly organised by Eugenie.
Sarah Ferguson will retain her royal title, the Duchess of York, despite the fallout.
A source told the Daily Mail's Eden Confidential column: "That has been her title since the divorce and that is how it will stay.
"Andrew is still the Duke of York, so it is not an issue."
Yesterday it was reported lawyers for Prince Andrew and Virginia Giuffre filed their initial requests for witnesses in her lawsuit accusing the British royal of sexually abusing her at age 17.
Recently released documents show that the prince's legal team is seeking witness accounts from her husband, Robert Giuffre, and her psychologist, Judith Lightfoot, as part of the civil case filed in the US.
Giuffre's lawyers, meanwhile, are seeking witness accounts from the prince's former assistant and a woman who claims to have seen him at a London nightclub with her during the time in question.
The lawsuit cleared a hurdle after a judge earlier last week refused Andrew's request to have it dismissed.
- Additional reporting AP
