If it's not too much trouble, perhaps you could give your full itinerary because it might be easier helping you figure out what makes the most sense. Also, it does help to know what your children like to do. For me, knowing my child, I know long days of transport is not high up on her list of things she likes. When I was alone, I day tripped from Kyoto to Fukuoka to see sakura. I would not do the same trip with my daughter even if it was sakura season.
I've not been to Ainokura, just Gokayama. Again it was pretty with all the snow, but I've not been in a rush to go back. I think @LikeBike and I agree about how awesome Hirayu onsen is, though I've not taken my daughter yet.
My daughter loved the garden in Kanazawa (another June 2018 visit), though her favorite of the well known gardens she has been to is Ritsuin in Takamatsu. If your children don't have one already, I found giving her a camera of her own has made a huge difference for travel. During her first trip at 5, she spent a lot of time saying she was ready to go when we were visiting temples and shrines. On her second trip at 6, she had her own camera and it has made an enormous difference. I really enjoyed Myoryuji (https://www.japan-guide.com/e/e4205.html
) Ninjadera in Kanazawa. My daughter did not. She wanted to actually try out all the ninja hiding spaces vs. just seeing them and hearing someone talk about them. We were there on a Monday so missed the Art Museum. I've been to several places in Kanazawa before she was born. Mine also loved just getting ice cream, they have gold leaf and platinum leaf ice cream there. It's cheezy but fun. One reason we didn't accomplish as much in Kanazawa was it was hot! It was more a dry heat than Kyoto (the same goes for Takayama) but it was still hot during the day. Kamikochi and Nagano were actually pretty cool. Matsumoto was hot our arrival day, but when we returned post Kamikochi it felt lovely.
This year we're trying more of Tohoku. Our current itinerary is: 5 nights in Kyoto with a day trip somewhere with my friend who lives in Osaka. (possibly Himeji, possibly the Expo Center, possibly Nara again.) I've been to Himeji and Nara multiple times, she's only been to Nara. We're then doing 3 nights in Sakurai to explore that area and to try ninja training. We're then going to Tokyo Disney Sea because we like rides, then spend several days in Tokyo before heading north to Hanamaki onsen and a self drive tour of parts of Tohoku. I really want to follow in @Mfedley's footsteps and visit the Osarizawa mine and I'm also attached to seeing the hydrangea forest near Ichinoseki and possibly the lavender fields near Yokote. I'm hoping it will be a little cooler in Tohoku. I've been to Towadako twice but not Tazawako.
We're leaving for Japan in the near future My husband doesn't travel with us, so it's always a compromise between planning for my daughter and planning for me. This is her 4th trip to Japan, and we always try to do a few big sights in Kyoto and mix it up with more low key activities. This trip we're looking into some craft classes. :)
I hope you find this helpful!