Why assume the machinations started with Harry and wife? I imagine the RFK and JFK organizations have a rivalry, and they could have engaged in a bit of one-upmanship.

The 2021 Earthshot Prize ceremony took place on 17 October 2021. Did the JFK people influence when the 2022 ceremony would take place and deliberately choose a date in early December, the period of time when the Ripple of Hope Gala is usually held?

Could the motivation behind giving Harry and wife the award be a need to slap back at Caroline Kennedy for hosting a rival event?

I doubt Harry's wife would agree to share any of the Netflix money with the Kennedys. Harry and wife don't have massive amounts of money to throw around - that's why they parted ways with Sunshine Sachs. They're not in a position to buy people and awards, but they are for sale, so it's more likely that Kerry Kennedy bought herself a prince than it is that Harry's wife bought herself an award.