I agree it would be difficult to kill her & get rid of the body with the 2 sons there....but I'm pretty sure the boys wouldn't be just right up dad's butt 24/7, they'd probably be off in their rooms playing games, watching TV, on their phones/tablet/computer or something, so it might be easier than one would think.
Here's a scenario to ponder: TK was in fact going through something, i.e....depression, anxiety, mid-life rut, maybe her periods were outta whack, OBGYNs can prescribe meds for depression, we don't know that she was actually seeing a psychiatrist. And her only seeing a doctor every 4 months tells me it wasn't that big of a deal otherwise she'd be seeing the doctor more often, monthly at least, why she sees a doctor at all is a mystery to us as we are only hearing one side of this story & marriage.
Back to my scenario....Maybe she found out P was having an affair &/or threatened divorce because of the affair or because she just wasn't happy. So PK thinks WTF am I gonna do, I can't afford to pay her child support/alimony (not sure if SC has alimony laws) then he remembers LIFE INSURANCE, so he comes up with a plan. He tells TK that he'll change do whatever it takes to make it work. He becomes very attentive to his wife, shows lots of love & affection (that way at least the kids see how much dad loves mom & maybe T tells a close friend how much he's changed) he may start doing the cleaning & cooking, since TK probably works til 7ish, nurses work 12 hour shifts normally (& wasn't he laid off around the same time or maybe before she went missing? Idk I'll have to look into that more) He starts tending to the kids more, cooks supper & feeds the kids but always makes a "special" plate for her to eat after she gets home. He could be doubling up her meds (maybe she wasn't taking the meds since she wasn't feeling so overwhelmed since he'd started helping out more so she wouldn't have noticed her meds were running out before refill time) or mixing some other substance in (antifreeze, rat poison or something to that effect, they do live in the country so it wouldn't be strange to have stuff like that around the house). T starts becoming sick & it may come & go depending on what & how much he's adding. T goes to work like normal that Saturday morning, she might mention she's not feeling all that great but not bad enough to call in, P makes her some coffee to go, adding in his "special" touch. By the time she gets to work & has drank her coffee it starts to hit her & she realizes there is no way she can work, as does her co-workers. T calls hubs & tells him to come get her, she's sick & dizzy & no way she can walk much less drive. He realizes this is it, his one chance alone with her that he can finish things. Maybe he packs a little bag on his way out with the PJs, remember he's been planning this out in his head. So he tells the boys "Hey Mom isn't feeling well I'm gonna run & pick her up, I'll be back." & he rushes to the rescue. He picks her up, then on the way home he does it, maybe he choked her with the seatbelt, Idk. He drives off to the woods, probably not the woods around their house, removed her scrubs & put on the PJs & leaves her there. He gets back home, goes in that back door or through the garage, boys are still in their rooms doing their thing, he brings her stuff in, purse where she normally put it & the scrubs, he throws them on the floor like she has changed clothes, makes the bed look like she's in it all huddled up under blankets & pillows snoozing away. Then after a bit he announces his, their, arrival home to the boys & says "Hey mom is sick & she's sleeping so we need to leave her alone ok?" Boys agree but then the younger one probably wants to see mommy or forgets his dad's request to let mom rest, tries to go in the room & dad thinks he's gotta get them outta there before they realize mom isn't in that bed. So he says "hey let's let mom rest & we'll go run some errands"; P probably makes a big show & says he's gonna go tell her they're leaving, so boys think they see her & see dad telling her they were leaving, but she was "resting peacefully" so they leave the house, taking her cell phone for whatever reason he gave, which unless they had a landline would have left his very sick wife at home alone with no way to contact him or anyone else if she started feeling worse & no way that she could've been contacted either. They run their errands, making sure to get time & date stamped receipts. They return home to find mom has vanished & there's a mysterious note from her, but all her stuff is still at home right where 'she' left it.
I'm sure P put on a good frantic show for the boys sake. And then calling the daughter in a tizzy, asking questions about mom.
I'm sure this is not spot on exactly & probably has some holes in it here & there but I'm thinking this is probably what happened. Keep in mind I haven't researched this a whole lot, just going by links that have been posted to the thread & the interview P did recently, that I still need to finish listening to. There is always something strange about the truth, it will NEVER change, but when someone tells lies, it will ALWAYS change, you can never remember which version you gave to who or to who you gave a different version.
The thoughts & opinions stated above are that, MY random thoughts & opinions.