That's a plan of attack, so to speak -- recommend these movies to Mom and let her decide. Perhaps she wouldn't mind the older films that haven't become so graphic like "Scarface," (was that the Paul Muni black-and-white version?) When I was young, I liked "White Heat," "Detective Story," and "The Asphalt Jungle."
Try the IMDB (Internet Movie Data Base) and put gangster into the search. It'll come up with a great list. Here's a link:
www.imdb.com