In August, how should I arrange transportation and accommodation for a 7 to 9-day trip to Tokyo, Mount Fuji, Osaka for shopping bags and Universal Studios?

In August, it’s my first time taking the kids to Japan. We plan to visit Tokyo, Mount Fuji, and Osaka to buy bags and Universal Studios. How should we arrange the 7 to 9-day transportation and accommodation?
Day 6-9: Travel to Kyoto and Nara by Shinkansen or plane. Upon arrival in Kyoto, check into a hotel, and visit famous Kyoto attractions such as Kiyomizu-dera Temple, the Golden Pavilion (Kinkaku-ji), etc.
Arrive by plane and check into a hotel in Tokyo. Stay at the Bulgari Tokyo, explore Tokyo from the 2nd to the 4th day, visit Mount Fuji on the 5th day, Osaka on the 6th day, and Universal Studios on the 7th day.
Osaka for Three Days: Stay at Ibis Kyoto Kyoto for Three Days: Stay at travellodge Shijo Karasuma Tokyo for Three Days: Stay at Shinjuku Shintetsu Hotel