hen isn't laying eggs. . .

[LithiumPyrite]

We have two hens that are 9 months old or so. Long story short, one hen adopted us so we bought her a Rhode island red for a buddy when they were chicks. The one that adopted us is laying beautiful eggs nearly every day but we have yet to see the RIR lay. However once a week or less a weird ugly egg shows up that we suspect is possibly from the RIR.
So the RIR is either not laying at all or she is laying ugly eggs with a weird weak stripe thing on them very infrequently. Any ideas? Here is a photo of two of the ugly eggs with the weak discolored part.