My father and his brother married two girls who were first cousins to each other. I know that the children from these marriages are not 'double' cousins, but they are genetically closer than simple first cousins. Is there a term for this relationship?
Aside from the generic "kin", the overly specific "first cousins through their fathers, second cousins through their mothers" and their consanguinity (15.625%) being slightly higher than for otherwise unrelated first cousins (12.5%), not really; at least not in English. For that matter, not in any other language I know, but there easily might be one which has a specific term for this kind of relationship.