In “An Apple Red As Blood”, Regina described the sleeping curse to Snow with the words “You’ll be trapped with nothing but your own regrets.” Perhaps in the dream each victim sees someone they have lost. Henry sees Emma (“she”) and Aurora sees Phillip (“he”). Presumably Snow would have seen Charming. But then I think the coincidence of Henry and Aurora having the dream at the same time suggests maybe they were seeing each other as has been suggested, and I agree that opens up a lot more possibilities for the plot!
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