I think Skyler's behaviour is perfectly understandable if you consider the developing of her relationship with Walt, whose behaviour is becoming more and more secretive day after day.
If at first the erratic mood of Walter was interpreted by Skyler and the closest members of the family by a more than comprehensible way to cope with the terrible news of the lung cancer that struck him, she starts to become angry at him the moment she feels that Walt is not being true, that he's hiding something and he's covering that something with lies (Walt's disappearance to hide the kidnap by Tuco, the fact that Gretchen and Elliot are not really paying for Walt's therapy, the second cell phone, Walt's fake visit to his mother).
When Skyler begins to understand that something is amiss, she tries to confront Walt but she only receives awkward lies instead of real answers from him. She doesn't know the truth but she sees right through Walt's bull**** (to quote Skyler).
At first she gets mad and angry at Walt, but since he keeps on acting as if everything is fine, although plainly in an unnatural and forcibly manner, she tries to provoke him in order to get the truth from him. When even this tactic fails Skyler becomes increasingly detached because she is simply tired of bouncing against the rubber wall of niceness and affability erected by her husband.
This goes on until Skyler receives the proof of her husband's lies directly from Walt, who gives himself away by revealing the existence of the second cell phone (that he always denied) when he's lying sedated in the hospital bed before going into surgery.
At this point Skyler can no longer ignore the truth and decides to confront Walt again, but she doesn't even give Walt the chance to explain himself because she is fed up with his lies ("Lies on top of lies on top of lies"). And when Walt desperately tries to stop Skyler from leaving him by offering her the truth, she doesn't even want to know, because now she "is afraid to".
I've loved Breaking Bad. I've loved the dialogues and the way the characters were "built" and shaped all throughout the series, and I do not see a shred of inconsistency nor an example of poor writing by the authors in developing Walt and Skyler's relationship, not in the second season and not in any other season.