I just had another look at your schedule and noticed that it's actually around 5 hours by train between Nikko and Kanazawa. Kanazawa to Hiroshima is another 4.5 hours which is a long day of travel.
Before I and others make suggestions - why do you want to visit Kanazawa?
Kanazawa is nice and all - but it's awfully out of the way with where you want to travel. You also seem to be spending a lot of time in temple/shrine locations.
Some are more fun for kids such as Miyajima. Others seem like a whole lot of temple/shrine hopping which will not be so fun with kids.
What are your interests? Do you like traditional places? Anime stuff?
I do like Koyasan - but will your kids be ok with eating vegan Buddhist food (mainly soy/mushroom based) with no real easy options for alternatives unless you bring it with you?
Moving around less with kids and doing more day trips would also possible be a good idea. Here is a good possible basic plan
Day 1 - 6 (Tokyo)
Potential long day trip to Nikko
Day 7-8 (Hiroshima)
Make the Tokyo to Hiroshima day an early one. Drop off your bags around lunch in Hiroshima and spend the afternoon at Miyajima.
Spend a day in Hiroshima and then go back to Kyoto
Day 9-15 - Kyoto
There are lots of great day trips in the Kyoto area. Some of my favourites include:
Hikone (nice castle - a good compact day which is not too far from Kyoto)
Himeji (another option of a castle and other stuff to do)
Nara. If I had kids, I'd probably stick to Todaiji Temple, Nara Park + Kasuga Taisha. I also personally liked the Nara National Museum which is a good option for wet days. Do note that you will get sick at looking at really old statues here!
Nagahama: A nice traditional town (with castle) which is less than an hour train ride from Kyoto. It's biggest selling point (when I visited) was the Nagahama Roman Passport - which gave you access to 5 location of your choice for 1000 yen. There was a lot of choices so you could visit a residence, garden, museum, castle, temple or figurine exhibition (which I would suggest for the kids). There was like 15+ places to choose from.https://www.japan-guide.com/community/mfedley/report-3378
I've heard that some kids like Toei Edomura (others call it a tourist trap so I can't confirm). Some people also say good things about the train museum in Kyoto as well. I've visited Disney Sea in Tokyo but expect long lines. In Tokyo - I also like things such as the Edo Tokyo Open Aire Architecture Museum or the Nihon Minkaen in Kawasaki (traditional building museum outside)