It appeared that Ben put that hat on for the paparazzi and the people with cell phones who were watching them from outside the store. He was probably trying to find humor in that rather than get upset by it like he did on their first honeymoon. Just staying on a private island in a private house would have been better for them, but at least one of them doesn't seem to have a problem with the attention.
He has a gambling addiction in addition to an alcohol addiction. He has lots of issues in his family. Obviously his brother has issues too. I have always thought Ben Affleck would be well off with a non celebrity person from his hometown. He is private and doesn't like or seek attention. He had a down to earth woman from West Virginia, he messed that up and she still took care of him for the sake of their kids. Then he proceeded to publicly disparage her and their marriage in an interview.
I think Ben and JLo are both people who think that other people can make them happy and solve their inner issues, and that never works. Just my opinion from the outside, obviously I don't know them and psychoanalyzing people you don't know is never appropriate. The Hallmark romantic story of getting married after all those years will wear off, relationships are work. She might think she can fix him too, that never works either.
"Those who do not remember the past are condemned to repeat it.”