Very weird! That's quite a contradiction, to say on one hand that she would NEVER EVER leave the kids and himself (not only the kids, but himself, he said) willingly, and on the other hand, be giving all these reasons for why she must have done just that. Right at the beginning, he was saying both. Maybe he was throwing both possibilities out there to see what stuck, and then when he realized people were looking at HIM with suspicion, he continued on with the story of her having left.
And if he truly thinks she left willingly, why not make a public plea for her to return? Even Ivy Merck's parents eventually spoke with Jane Valez Mitchell and pleaded with their daughter to come home. Seems like he'd be begging for JR to come home, for many reasons - for the sake of the kids, so that he would no longer be under suspicion, and because he'd be worried about her safety.
He keeps insisting that he's working with authorities, and doesn't want anyone to do anything to hinder the investigation. This statement is very convenient for him, because a) he portrays himself as being fully cooperative, and b) he doesn't have to do anything extra to find her (no PI, no press conference, no public pleas, etc) because it's not what LE wants. Very convenient.