My thoughts...
Might have gone home to have it out so to speak, finding her not there, he just left knowing the kids would be home soon.
Might have been making a statement with the wallet and cash, may have had a spare ID. Could have locked the door on the way out and taken the keys with him.
Not all missing people contact LE to alert them. If he's across country and not internet-friendly, he may have no idea what's going on locally.
I would think he would have had to have been saving or have his own private bank account to finance this.
The club being missing is the one thing that leaves a niggling doubt in his escape from his life because I can see someone attacking him with it. Although if he no longer cared about his life/car, he could have just chucked it into a garbage can at the train station.