So it all hinges on this scene...

Let's imagine that when he was leaving her house to go see his Son, and she says 'get yourself some water so you don't get dehydrated' - that he took his bag with him. She would not have been able to steal his tablet. 'Oh damn - I guess all that time I invested in this counter-con was wasted.'
He gets to keep his money.

Such a weak premise for the whole movie to revolve on.

He would definitely never leave that bag out of his sight, because you expect the world to treat you as you treat it.
And he sure as hell wouldn't have ridden that whole time on the train without looking at it, and not realizing until hours later.