To drive or maximise the use of JR Pass

Hi, we will visiting Kyushu next month, it is our first visit to Kyushu and we will be staying 4 nights. Intended itinerary as follows:
Day 1 Arrive Hakata, travel to Yufuin,stay 1 night. Possibly visit Beppu

Day 2 Visit Mt Aso and Kumamoto, stay 1 night at Kumamoto

Day 3 Travel to Nagasaki, stay 1 night

Day 4 Travel to Hakata, stay 1 night

As we will be using the JR Pass to travel from Osaka to Hakata, just wondering if it makes sense to spend more money to rent a car for the above itinerary or just maximise the use of the JR Pass.There's 3 of us.

Would it be relatively easy to move among these places by train/bus? Would appreciate any advice, thank you.

It's hard to say, and since I've never visited Kyushu, please take my comment skeptically and with some suspicion, but I personally always prefer to drive if I can! Driving gives you a lot more flexibility than public transportation, and also you can carry more stuff!

But if you already have the pass, then it is definitely possible to get around using shinkansen or major railways, so if you're looking to save money, then I'd stick with trains.

If you visit the Japan Guide page on Kyushu, you can see the shinkansen route in red, and the major train lines in orange. Getting to Oita means probably traveling to either Kumamoto or Kita-Kyushu first then transferring. I think if you want to go to Yufuin first you should not go to Hakata and instead transfer at Kitakyushu. Then you can go from Oita to Kumamoto with a stop at Aso on the way. There are probably bus routes that are more direct than the train to Nagasaki, but I'm not sure what is available, so I'd check around. Then Nagasaki back to Hakata is easy enough.

Thank u so much scareddragon! Even though u have not been to Kyushu, I appreciate u sharing your view. Cheers!