Tateyama Alpine Route cannot booked in advance, it does not had any entrance ticket.

You need need is buy transport ticket only.
May are Opening Season, Get ready for extremely crowded in line to boarding those Cable Car, Buses etc etc. each transport minimum 10-30 minute waiting.
Since you already got JR Rail Pass, I no recommended to get Alpine Tourist Pass.
Toyama Station > Tateyama Station with Toyama Chiho Railway - 1230 Yen
Tateyama Station Bijodaira with Tateyama Cable Car - 960 Yen (10-15 minute waiting in line) *This will depend how much people riding Chiho Railway with you
Bijidaira to Murodo (Snow Wall) by Bus - 2200 Yen (10-15 minute waiting in line) *This will depend how much people riding Chiho Railway with you
Murodo to Daikanbo by Trolley Bus - 2200 Yen (This part are most congested waiting in line to board that Bus)
Daikanbo to Kurobedaira by Ropeway - 1320 Yen (10 minute waiting usually)
Kurobedaira to Kurobe Dam by Kurobe Cablecar - 1050 Yen (10 minute waiting usually)
Kurobe Dam to Ogizawa by Kanden Tunnel Bus - 1570 Yen (10-20 minute waiting)
Ogizawa-Omachi Bus - 1390 Yen (10 minute waiting usually)
By the Time you reach JR Omachi Station will be sunset already and reach Matsumoto Station will be dark.
If you from Tokyo going Nagano first (Snow Monkey) + Kamikochi then route above with be terbalik

you end up at Toyama Station. The waiting time need add extra 10% because most Japanese like going Alpine Route from Omachi > Tateyama Station.
From Tateyama > Omachi are mostly Foreigners & Chinese Tourist because they go Takayama + Shirakawa first.
Shirakawa can advance booking from Alpico / Nohi. (I usually booked from Nohi because it just beside Tayama Station)
Kamikochi are Hiking trail. You going with Family. Can forget about it. Your kids cannot stand the wind chill temperature + hiking (need alot stamina)
If you die die must go, then from Matsumoto Station / Nagano Station take Express Bus to Kamikochi Bus Terminal. Bus ticket can advance booked from Alpico.
*Seriously not recommended for you!*
Nagano Snow Monkey are public bus. From Nagano Station take Private Line "Nagano Dentetsu" Limited Express to Yudanaka Station. From Yudanaka Station take Public Bus to Shigakogen Roman Museum and walk to Snow Monkey Park (Follow the Direction Sign / GPS) or Take Taxi (1000 Yen only)
*Warning!!! Do not wear sneaker!!! Wear only Boots. If you ca't find boot for your children then forget about this snow monkey)
Wear Sneaker, you are cari mati with frost Bite.
For Tateyama alpine, Yeah it’s just transport but can book advance? If I can buy all the tickets in one shot all the way to Kurobe dam and back to Tateyama then will save time queuing for ticket.
Toyama - Tateyama alpine day trip, Looks like need to start very early to beat the crowd… tickets can only be purchased from Dentetsu-Toyama station?
I can’t move the hotel dates in Takayama because I was able to book at reasonable price
The Kamikochi trek really that challenging? My son I don’t worry as he hike with us in Melbourne previously to mount Oberon, 8.8km return, very proud of him
It’s the other family I’m more concerned, I better ask them to look at the trail first because total walk is like 8-10km, thanks for the warning bro