Road Trip from Fukuoka to Kyoto

We (a family of 5 adults) will be visiting Fukuoka come 03.08.23 and follow the suggested 5 days 4 nights Itinerary. We plan to rent a car throughout this journey up to Kyoto. On the 6th day, we will head to Kitakyushu, Hiroshima, Okayama, Himeji, Osaka & Kyoto (8 days all in). Will drive back to Fukuoka and spend a day before flying back home the following morning. Is it ok or advisable? Kindly advise.

I'd do one-way at most, Fukuoka → Kyoto, drop off the car in Kyoto and take the Shinkansen back. Personally though I'd just take the train all the way.

We (a family of 5 adults) will be visiting Fukuoka come 03.08.23 and follow the suggested 5 days 4 nights Itinerary. We plan to rent a car throughout this journey up to Kyoto. On the 6th day, we will head to Kitakyushu, Hiroshima, Okayama, Himeji, Osaka & Kyoto (8 days all in). Will drive back to Fukuoka and spend a day before flying back home the following morning. Is it ok or advisable? Kindly advise.

Let me see if I understand
Day 1 - 5 you are somewhere in Kyushu driving around
Day 6 you go from Fukuoka to Osaka and plan to visit a bunch of places on your way
Day 7 in Kyoto/Osaka
Day 8 driving back to Fukuoka
Correct???

If so, this plan is crazy.
Day 6 is undoable. Fukuoka - Kyoto are 8 h driving. Plus add a few breaks for lunch/ toilet and you are talking about 10h. Only the driving. No time to do any tourism. Day 8 will be the same.
Fukuoka - Kyoto by Shinkansen however is 2:45 - 3:00 h. You can do SOME tourism that day but not everything you listed.

If instead your plan is to travel slowly by car from Fukuoka to Kyoto and arrive on day 8 in Kyoto , return the car there (attention additional charges) then that is doable.

Still wouldn’t advise doing it, as all the places you listed are easily accessible by Shinkansen. No slow city driving, high parking fees, …

Not advisable.

All locations are easy to reach.

About 750usd in expressway fees.

Last day is 1000km / 11-12 hrs in car without stops.

In Fukuoka, I strongly recommend you to buy
Fukuoka Tenjin to Dazaifu unlimited bus pass =820 yen,operated by nishitetsu

Driving can make sense if you are going to places not easily accessed by trains or buses. As for driving one way, you also would have to check if there are drop off charges for that - they can be very, very expensive at some places.
I suggest you consider the JR Setouchi Area Pass if you want to go both ways.
https://www.japan-guide.com/e/e2361_setouchi.html

You could also give more info on your plans for Fukuoka and/or Kyushu. There is a lot to see though.
https://goo.gl/X3LDaE