The issue isn't the use of conflict as a dramatic device per se; it is essentially forcing the player(s) to perform a seemingly unnecessary and unpleasant action against their will.
The fact that both main characters in the game appear to immediately decide that violently murdering their child's favorite toy is the only course of action and that no alternative is offered is really jarring. Giving the player some agency in choosing an alternative way to to go about it would have solved the problem completely.
Yeah, you've pretty much hit the nail on the head. After hearing the dev's justification I can see what they were going for, but it's really poorly handled in-game IMO.
They way it plays out in the story feels neither darkly comic nor a poignant commentary on parents going though a divorce; instead it just comes across as unnecessarily cruel, and the player has no choice but to go along with it.