I couldn't find my way around their website
I am not even sure if this a coach you can book exclusively for your family or it's a play area on the train but it's a great way to travel with children, I first found about it on this page
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Each playroom coach have 4 regular seats that can be reserved, no surcharge applies. Just book your ticket normally at the VR Shop, making sure to select one of the trains equipped with a playroom of course. Look for the little teddy bear icon next to Services:
Then "continue to seat selection", and request a seat "Next to Playroom":
Note that you don't have to book a seat in that section if you want to use the playroom, and for your sanity you might not want to! All kids are welcome to use it.