Maybe the reason this escalated is the habit of many airlines to offer to sell replacement tickets (for lost paper tickets, for example) as last-minute, one-way, full-fare tickets. (Even when the ticket being replaced was a deep-discount ticket, which I would bet was what this family was traveling on).

If that is what happened in this case, the parents probably balked - full-fare on this route is certainly a number that would make many people balk.

Depending on the other questions raised above, NW - while technically correct - may have handled this at the airport in a way that caused escalation and this eventual outcome.