I'm curious to know what the shared DNA would be between half-sisters who are also first cousins. If the mother of both sisters had an affair with one of the sister's father's brothers what would the shared DNA look like? Full sisters? would they still share a full X?
Overall the amount of DNA half-sisters/cousins share would be expected to fall about halfway between the amounts that full sisters and half-sisters would share, but because of the randomness of inheritance it would be difficult to distinguish the actual amount of sharing from being in the possible range of sharing for one of the two more usual cases (full or half siblings). In fact, the possible ranges for full and half siblings even overlap, and so some shared amount results can't distinguish between those two cases; the intermediate case of half-sisters/cousins would have a much wider range of range overlap with the usual ranges and thus be more ambiguous.
In the special case of their X chromosomes, one would likely be able to tell the difference between full sisters and the half-sisters/cousins. The fathers who are full brothers are very unlikely to have identical X chromosomes; they each inherit a random part of their X chromosome from their maternal grandfather and the rest from their maternal grandmother. Hence the paternal X that each half sister inherits from her father is unlikely to be very close to identical with the other sister, and so they would be very unlikely to show as sharing a full X chromosome (as full sisters would).