Now you're getting into the real forensics, Janus!!! IDK how exact science is on determining time of death. Guess this is where the phrase 'suspension of disbelief' comes in. My big 'thing' is WHY would Katz (a policeman) leave his own weapon at the scene of the crime. That (to me) would make me think that he didn't do it, that it was a plant or someone stole his gun.
I originally thought that Jo was going to try to make it look like a suicide, but I assume the gunshot wounds wouldn't bear that out. I think her overall thought was to just get Adam out of there before anyone showed up and then let the chips fall where they may. If they pointed at Katz, all the better. And there's really no saying that she hoped/expected the bodies to be found right away. It may be that she actually hoped it might take some time, the better to make it harder to determine TOD. The natural timeline for discovery would be Tripp going missing, wife files report, search initiated, car found, search of woods, bodies found. Or someone just reporting an abandoned car in the carpark in the woods etc etc. Either of those would take, what, a week? Maybe Jo was going to call in an 'anonymous' tip.
I think Jo would have convinced Adam that it was far better to leave Corinne there than to risk the boys losing both of their parents (her to death/him to prison).
On one hand it's fun to 'pick apart' a murder mystery. On the other it ruins the satisfaction of the resolution. Double edged sword.