I know it sucks when you have to remain calm. But if we don't we're kind of being hypocritical.

I do the sit on the couch until you sort it out thing. And when they were little I would guide them in how to talk about how they feel and how to come to a resolution. It works. The first few times might be a battle of stamina. As they'll probably just want to call your bluff but when they realise they can't continue playing/eating etc until they have reconciled you'd be amazed at how quickly they learn