The son, whose name was Arthur Marston, painted a picture for my grandmother, which she kept. This is it:
It measures 7 inches by 5 inches, and has a couple of creases in the top-right and bottom-left corner, but otherwise it's in quite good nick.
He went on to become a minor artist of note, but not professionally. See https://artuk.org/discover/artists/marston-arthur-19021984 for two that are on public display.
Unfortunately, it's really hard to find out much about his other works because Arthur Morgan and John Marston are main characters in the Red Read Redemption franchise.
I don't know if this one is by him too https://www.mutualart.com/Artwork/Youth-seated-beneath-a-tree/, but if it is it might explain why his relationship with my grandmother came to nothing.