Combine Okinawa Islands with Hokkaido

We just returned from our second travels to Japan from Belgium and cannot get enough of Japan so we already started planning our third visit.
Our first trip included Kyoto (region)/Hiroshima/Japanese Alps/Tokyo (region), all done using public transport. The second trip this year started with a self drive around Kyushu and then taking Shinkansen to Osaka and Kobe region. After that we took Shinkansen to Tokyo and ended with 5 days staying there. Both trips were 3 weeks.
We now plan to go back to Japan next year during last 2 weeks of June, first week of July and wanted to combine Hokkaido and Okinawa Islands. We really want to rent a car again, especially Hokkaido, but maybe also Okinawa to travel around.
Not really sure how to start planning this trip, f.e. about 10 days Hokkaido, fly to Okinawa and plan also about 7-10 days? Maybe at the end of the trip fly back to Tokyo for about 3 days to visit some things not done before and fly back to Brussels?
All info to help planning our trip would be absolutely welcome here.

Mid to late June is good for Hokkaido while late June to early July is good for Okinawa (after the rainy season, that is).

I would fly from Haneda to Wakkanai, spend about 5 days in Wakkanai/Rishiri/Rebun area. Then drive south to Sapporo for 5 days. Sapporo by itself is not so interesting.

There are flights from Tokyo to Wakkanai and Sapporo to Okinawa (Naha, OKA) both of which is 97.42 USD for foreign tourists. After spending 2-3 days in Naha, fly to Ishigaki (69.12 USD). Enjoy Yaeyama islands for 5 days and then take direct flight to Tokyo (Haneda) (97.6 USD). At present ANA does not show direct flight from Ishigaki to Haneda for early July, but it might open the flight later this year (or next year).

Or you can do the trip the other way round. In that case you might encounter rainy season in Okinawa, but it tend to be less crowded.

In any case, mid June to early July is not good season for most of Japan, but as for Hokkaido and Okinawa, it is one of the best season. Enjoy planning and have a nice trip!

Okinawa at that time is the rainy season, but no one knows at what day it will end.
https://youtu.be/xHh_ugwcMto

Not sure why frog1954 decided to quote prices in USD from ANA's US website, seeing as OP is from Belgium. Besides, Naha to Ishigaki can usually be had for JPY 5,100 (from the Japanese website).

Rainy season in Okinawa usually finishes between 20th to 25th June. The Youtube video says it finished 22th June last year. But of course it deviates in each year.

Thanks to all for the advice. We were not sure if Hokkaido and Okinawa (Islands) could be combined in 1 trip. But it seems they can. Would you advise a rental car on the Okinawa (Islands)? Or is there enough public transportation/tours?

Would you advise a rental car on the Okinawa (Islands)?

Well, it depends where you want to go. If you stay in Naha, mainland Okinawa and want to visit within Naha (there are much to see, but they are cultural things), Monorail would be enough. But if you want to travel around the main island, you should rent a car.

In Yaeyama islands, you might take day tours and don't need rental car during the tour. If you want to see by yourself, you may better rent a car. I would rent a car one day in Ishigaki and for other days do day tours to Iriomote, Taketomi, etc.