I've started watching the show from the beginning and my disliking of Skyler has increased significantly. There is an episode of Season 2 where Walt is trying to make Skyler feel at ease about a 2nd cellphone. He's is lying of course, but up to that point of the show I believe Walter still has good intentions for her not to know - he's trying to protect her and his family. All she knows at that point is that Walt has Cancer, and he likes to spend time by himself. She has some suspicions about the cellphone, but she knows nothing else.
However, I just can't see how she makes the leap of logic to punish Walt, given that from her perspective Walt recently went missing, and doesn't remember what happened to him. If I was her, the only thing on my mind would be that my husband is going crazy. But how does she react? Not by being understanding, but by acting up, by leaving the house without telling Walt, by being in a "bitchy" behavior all the time. Walt has Cancer - that's his excuse. What is hers? Maybe it's just me, but when I have a problem I focus in resolving that problem, instead of creating more conflict that will lead to more problems.
Then to top it all, Walter gives in and tells Skyler his is sorry for whatever reason she has to be mad at him. He makes a concerned effort to find out why she is pissed off. But she decides to create more conflict.
*no spoilers for anything up to, and including, "Down"
Prior to the show, her relationship with Walter was presumably one where she was the dominant figure in the relationship, both of them quite open to the other. After the show begins, in the very first episode, three weeks pass in which Walter is rarely home, barely communicates, and when he does he gives her extremely flimsy excuses which she sees through. At the very end of the pilot she says:
"Walt, I don't know what's been going on with you lately but, whatever it is, I'll tell you this, I do not like it when you don't talk to me. The worst thing you can do is shut me out."
This is something that, for the entirety of the season(s), Walter does. His lies are incredibly transparent early on (when Jesse calls in the second episode for example, Walter's lie is blatant; this occurs after three weeks of barely any communication with Skyler being absent from his house at a plethora of times, something she has already picked up on) and she is not a fool, she can see through his lies (she cannot see the truth, but she doesn't believe everything he says without question).
Walter has cancer, and he claims to enjoy spending time alone, but this doesn't excuse his behaviour. From her perspective, he is gone from the house at all hours, without any sort of reason or explanation where he was gone, completely unwilling to talk about what he was doing except in the vaguest terms using flimsy lies; coinciding with a drastic change in activity and behaviour which he 'shuts her out' from, he isn't willing to communicate about how he is feeling or what he is doing in the slightest. Walter having a good or bad intention for not letting her know is irrelevant. Skyler isn't a mind reader and it's ridiculous to expect her to know if his intentions are good or bad (although I would completely disagree that not letting her know is a good thing in the first place but, again, this is irrelevant to Skyler). Skyler has already openly discussed how she strongly dislikes being shut out and how she wants to be included in Walter's feelings, but he resists her at every single turn and she isn't stupid enough to fall for every one of his excuses. She does in fact back off after "A Crazy Handul of Nothin'" (where he mentions that he likes to be alone), but after "Grilled" she sees right through it (we know she backs off as after Walter attempts to rape her she references his feelings with regard to the cancer as the reason).
At "Grilled", Skyler doesn't suspect he has a second mobile phone, she knows he does. Hank outright says there's no record of the phone call, to which he says "he must have a second phone". Skyler wonders why, and Hank replies that it means "Walt has a secret". As if that wasn't enough, Marie rightfully comments that "he kept cancer from you, for weeks". As she asks Walter about it, he makes excuses, and lies, which she she easily sees through. She absolutely knows he is hiding something from her, and that he is shutting her out, she just doesn't know what it is, which she wants to know. On top of that, he is demeaning to her in his excuses and lying to her as if she is a fool. Walter did go missing, but there wasn't any actual reason why he went missing, or why he wouldn't remember. He had put her through considerable worry (which we saw, and he saw) during the disappearance, acting extremely odd beforehand, and she knew that his medication had nothing to do with it. Perhaps you would openly accept that somebody is in considerable distress, gets a call from a secret mobile phone, vanishes from the house for a considerable length of time, returns home, and there is no explanation as to what was the cause (and lying considerably about some of the details which she is aware are lies), but I am pretty certain most people would be somewhat suspicious.
She leaves the house not to 'punish' Walter, but to show him what it feels like to her (for the last few months/weeks). She leaves the house all day, without mentioning where she is, giving a flimsy and vague excuse while being emotionally distance, just as he has been doing. We have seen with Marie how much she despises lies (illicit behaviour too as she . Cancer he may have, but it doesn't serve as an adequate 'excuse' for how he's been acting for months; he doesn't exist in a vaccuum. She doesn't just 'create conflict' for the sake of it, she has, time and again, tried to figure out what's going on, and every single time Walter has shut her out. She had somewhat accepted that he liked to be alone, but knowing about the secret mobile phone completely shattered that excuse as it begs the question 'What exactly is he doing in his time alone?" Walter doesn't make a concerned effort to find out why she is annoyed, he knows full well, and blatantly lies to her face about something she knows is true.
When you add up:
Disappears from the house without any apparent reason.
Leaves at all times.
Likes to spend time alone.
Has a second mobile phone which he lies continuously about and makes excuses for.
Lack of willingness to communicate.
Continuous lies (which she knows are lies).
Drastic change in behaviour at home.
You get more than enough reason to be suspicious. EDIT 3: It isn't even that she knows he's doing something 'bad', it's that he is shutting her out and acting as if she doesn't even exist, being emotionally distant and cold for months, completely unwilling to communicate.
EDIT: I hope this helps to explain Skyler's reasoning. I generally get involved in Skyler-related discussions if I'm quite honest since it's a topic regularly brought up here but I'm hoping it clarifies her behaviour enough to increase your enjoyment somewhat (by making it more believable/understandable or otherwise).
EDIT 2: Oh and you really should be avoiding this thread in all honestly since there are unmarked spoilers up to the twelfth episode of season five and you absolutely do not want to be aware of characters that are still alive, what is currently happening, or events that have happened after the episode you are on but before the current season and it may considerably reduce the tension to you within the show.