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Back to the original topic, I don't think it is possible to have an identical twin cousin, unless through some crazy-assed inbreeding you get someone to be your sibling and cousin. Otherwise I'm pretty sure it's impossible.
I just discussed this with my grandfather (who knows a lot about biology and such) and he said that the two children would technically be cousins, but be more genetically similar than normal cousins would be. Genetically these cousins would be more like siblings. However, I contend it would be pretty unlikely they would look identical. Due to the separation. I would bet each couple would be more likely to produce identical twins though. The two children (cousins) would probably look fairly similar, like normal siblings do, but they could also look completely different.
Funnily enough, we do have a second cousin who looked exactly like my brother- at first I thought it was him - but we only found out after looking at family albums of the Norwegian side of the family. They weren't the same age at the same time so no one noticed til I pointed out the photographs years later. They never met.