You cannot trust anyone, and that's very sad & scary.
This is what gets to me about this case. There is actually very little information, especially if you discount the husband's story. Obviously LE can't disclose much, but usually there are more people close to a person who have strong opinions and speak out, or at least more witnesses.
PK seems like a very open and likable person in all of the interviews. His charisma was certainly what got LE involved quickly in the beginning and helped to draw attention to the case at first (and for those who have said that he called right away, if he was responsible then that call was far from right away). What's disconcerting is how much he has been allowed to set the narrative in a relative vacuum. It's very convenient that he has stories that compliment what LE has disclosed (such as the emotional cheating) but that take them that much farther. I agree that his behavior has been odd, and although resentment in a spouse who has been left with the full load of responsibilities is common, he certainly can't manage to fit enough character assassination in (did you know she was an alcoholic, cheater, detached and distant mother and spouse, fighting with her children, recalcitrant and refusing help or medical attention, suicidally dangerous, miserly...and I'm sure I've missed some...) and that's a very troubling response to your life partner vanishing.
Also, perhaps my timeline is off, but it does seem strange that in the interview he'd say something like "that's the last time we saw her alive" (!) as if he has some insight while the rest of her family holds out hope as people tend to, while simultaneously calling all of his children to go find their mother after she goes missing (as has been mentioned). He has quick and convenient explanations for everything (he's afraid of lie-detectors! his son is a boyscout!) but they are unprompted details that don't make sense of anything. Also while most people would feel immense guilt at the potential loss of a partner, this guy is full on the defensive: claiming to be ridiculously sweet and blameless in response to her behaviors (though all of the photos I've found show her and the kids smiling but not him, she seems like the appeasing one trying to get everything to work), meanwhile laying out all of these wild unsubstantiated accusations against her as if they're fact (of her drinking, cheating, multiple suicide attempts without hospital admissions, serious mental health crises, etc), using language that includes his alibi (the kids) in every possible place.
I think all of this is questionable enough, but if you consider how little we know without his narrative, it really highlights how much everyone has been relying on him to flesh out the details. Without his story, all you have is that she left her car at work and came home early, on her phone were deleted messages of a flirtatious nature to a couple of other guys from an unknown period of time, her phone moved around the area, later that day one son cut his grandmother's grass and another accompanied his father on errands, later a phone call went to the daughter and eventually to the cops, her phone was not used, searches turned up nothing. That's it. Even some of that hasn't been substantiated be LE. All of the relative positions of those people and most of the day are unaccounted for. PK has convenient information to fill in all of that, and even people here have just been assuming the things that he has said are correct. But his answers have changed.
Also in the interview, she said something like "you're a smart guy, you would generally consider yourself intelligent wouldn't you?" (not exact words, here) and that was the only time I noticed him pause. He has answers for everything, he'll interrupt to correct you and set you straight on things. He's eager to talk about it. But if it doesn't fit with how he wants to be seen, and he wasn't expecting the question, suddenly he doesn't know what to say. Someone not wanting to acknowledge that they're intelligent, even for the sake of conversation, speaks volumes to me in this context. Even though some of his intellect is clear, he wants to be seen as the goofy hapless father figure who is a victim in this situation. Why would that be?
I went in really believing that he had nothing to do with this. Hearing some of the phrasing he used in that interview, and some good points added here, I'm less and less sure.
Finally, here's what linguistic text analysis on lying tells us:
1. People who are lying tend to use minimal self-referencing. They mention themselves less often, other people involved more often, and tend to speak in the third person.
2. They tend to use negative language, stronger language, and cast aspersions on other people or objects (ex. "My stupid phone died, I hate that thing.").
3. When lying, people tend to explain events in simple terms. Most people are very bad at constructing a complex lie.
4. But when discussing the situation they tend to use longer, more complex, and more convoluted phrasing and sentence structure. They use unnecessary words and add in irrelevant but factual-sounding details.
I hope that this outline might help you in thinking about other cases as well. Does any of that sound familiar to you with this case?