Faye is just being a mugwhump right now. i think she's in that point in facing her drinking problem where it's making her just extra grumpy. No excuse really, but it does explain her sudden mood swings.
Claire is an unknown factor in her life at the moment. Granted, she's Martens GF, which gets her in the door (so to speak) with Faye, but she's not really had much contact or dealings with her on a really personal level as she is now, so she's feeling defensive, probably another part of her current mood set after the 'Crash'.
Claire doesn't really know Faye all that well either, despite recent contact and what Marten may have shared with her, so she's not quite figured out how to properly react around her. Then too, I don't thing Claire has had much in the way of social contact in the kind of context she's in now. Granted, she's no Marigold, but neither is she used to that kind of contact and hasn't quite figured out the rules yet.