I've traveled for 3 weeks in July/Aug 2019 with kids.
The Japanese humidity really is different from the Spanish Sevilla/Granada 40C dry heat, i've experienced both :)
You will probably be sweating from the very second you step out of your air conditioned hotel, so make sure to bring enough water with you.
Your travel plans seems to be relaxed enough.
I would agree with most that the Hiroshima part could be shorter or changed a bit.
You could consider the following destinations:
In between Tokyo & Kyoto is Kakegawa, with 2 things great for kids (and adults)
There you can find a great Flower and Bird Park (Kakegawa Kachoen) and Kiwi Fruits Country farm (~10 min by taxi) where you can pick tea and kiwis. Very educational and tasty! (kiwicountry.jp)
In between Kyoto and Hiroshima you could add a stop?
Himeji - visit the big castle (visit as early as possible)
Okoyama - Korakuen garden + castle
Kurashiki - Canal town
You could consider staying the night on Miyajima island, most places offer a Ryokan stay?
That way you can visit the shrine at night at ease, very recommended.
Going to Miyajima you can take the cable car to the top of Mt. Misen and walk down if you have the time, the view is spectacular. And dont forget to visit Daisho-in temple, its about 5 minutes walking from the center of town.
***some general things ***
You could view Kyoto as having 2 parts.
The east side (to the right of the Kamo river) has a lot of temples that can be visiting in one day just by walking. You can walk in a straight line almost from Ginkaku-ji to Kiyomizu-dera for example.
For the northwest part of Kyoto I would recommend renting an electric bike if the kids are old enough. (https://kyoto-option.com/
By bike you can hit all the highlights of that part in a day.
One maximum temple route could be Kinkakuji, Ryoanji, Ninnaji, Daikaku-ji, Otagi Nenbutsu, Gio, Arashiyama Bamboo, Tenryu/Shigetsu, Togetsukyo bridge. Skip some temples to save time and prevent temple burnout :)
Otagi Nenbutsu is a bit out of the way, but special, so try and visit that one.
Fushimi Inari is quite the hike if you want to go to the top, so its probably better to visit at night?
Could even be spooky fun for the kids!
--When visiting Tokyo try the Cup Noodle Museum in Yokohama. You must make reservations in advance or arrive really early!
MORI Building DIGITAL ART MUSEUM in Tokyo is also great interactive fun with the kids.
The Tokyo Metro building is the best free observatory.
And if you really want to visit a Disney park then go for Disney Sea. Tokyo Disneyland is the same as the one in Paris :)