Kyushu-- JR Pass and Gen. Travel Tips

Hello,

I'll be spending three weeks in Tokyo and 1 week in Kyoto before my mom joins me in Japan. Then, we'll be traveling together in Japan from June 24th to July 6th.

For this later part of my trip, I am a little unsure about a few of the logistics, such as amount of time to spend in each area (especially for the Kyushu part of the trip) and what to do with our luggage (maybe which places would make sense to book hotels/stay overnight).

Additionally, for the Kyushu part of our visit, I am confused about whether it would make sense to get a local JR pass, and if so, which one (should we do 3 day Southern Kyushu pass or 3 day all of Kyushu pass or something else).
I have made a rough outline of places I'd like to visit:

Kyushu:
-- Fly down to Yakushima from Tokyo. Spend 1-2 days in Yakushima -- Take a ferry to Kagoshima. Spend 1-2 days around Takachiho Gorge area -- Visit Oita/Beppu. (Kokonoe Suspension Bridge and Hells of Beppu hot springs). 1 day -- Fukuoka. 1 day

Leave Kyushu:
-- Shumanami Kaido (1 day) -- Hiroshima. Taishakukyo Gorge, Taishakuten Eimoji Temple, Ueno Pond (1day) --Osaka (1 day) --Kyoto (2+? days) -- Return to Tokyo (1+? days). Depart Japan

Any advice would be greatly appreciated!
Thank you for your time and assistance,
--Ritu S.