I think that I saw kids in the Alps maybe once – in Japan it tends to be an activity for older people. That said, I would expect that the huts would charge for each person, regardless of age, and I don’t recall seeing any discounts for kids – but not that I was looking. You don’t say how old your kids are, but the other thing to consider is that a lot of the Alpine routes are very exposed and I’d hesitate to take kids on them, whatever the age. However, there are plenty of really good, safe places to hike with kids – for example, we took our kids (they were 3/7/11 at the time) to Kamikochi, which can be reached by public transport, and then walked up the valley to a place called Tokusawa where they actually rented out family sized tents on a big lawn. It was a really scenic area and the hut there – which is quite famous – had good meals, if you weren’t inclined to cook. From there I did an overnight trip on my own up to Yarigatake, which is further up the valley. There are also lots of daywalks around Tokyo and Osaka. There’s also more info available from the Japanese tourist websites now too than there used to be.
Edit – the prices for staying in the huts usually include two meals. Have a look at my trip report for Yarigatake to get an impression of what the huts are like.
I hadn’t realised that they hadn’t updated the Lonely Planet book since 2009, but a lot of their walks were off compared to the routes that the Japanese guide books suggested and I genuinely wondered if they’d actually done some of the walks. I showed a few of them to a Japanese friend who owns a hiking shop and run trips a couple of times a month and he really wasn’t impressed. The 1988 book is, I think, the original Lonely Planet book and has odd attitudes to Japan and used to trigger a lot of complaints, and was also out of date even back in the 90s – famously it suggested a stay at a hostel near Tokyo that closed in the early 80s! It also got a mountain name wrong, which confused my friend when I was telling him where I was intending to walk …..