Here's my theory. She was planning on divorcing him and was seeing another man. She either told Josh her intentions of divorcing him or they some how got into a big argument. He doesn't have family in Utah and no where to go so out of spite, he takes the two kids and leaves to get away from her. She is finally sick of it and ups and leaves with this other guy and disappears.
In regards to the wet carpet spot, maybe during their argument a glass was thrown or spilled or dropped. Both upset, didn't want to take the time to clean it up so they just got a towel and put a fan there. Or maybe one of the kids spilled a drink right before he was going to take them and he wanted to leave right away and didn't want to spend anymore time cleaning it up. They never found any traces of vomit or blood on that carpet spot.
Or, maybe she did run off with another man and this guy wanted it to look like her husband killed her so they planted that there. Basically framing him. People say that would never happen but some people have mind control over others and if she is seeing some one new, most people will do anything because they are happier with that new person.
As far as the rental car goes, we all know the police took Josh's car away from him and he was forced to get a rental car. Maybe he knew about this other guy or found something that lead him to go to Ely, Nevada to look for her so he got a car and drove there to see if he could find her because he was worried.
People say Josh hasn't been cooperative, well....that's what the media tells them. Maybe he has told them everything he knows and the police want more but he has nothing else to give them. So that's why he up and moved to get away from it all. If he's innocent, that would be hell to go through.
As far as the restraining order he has against her family for the kids....Makes sense. If you had kids and were being wrongly convicted by your family that you murdered your wife, would you want your children to be around them, feeding their minds full of things? I know I wouldn't. And kids get pressured into saying things when adults want answers.
I'm most likely very wrong with this whole thing but I tend to give people the benefit of the doubt when the proof is not there.