The Rockefellers were almost certainly the richest family.
#2 probably would have been the Morgans or the Duponts, who had expanded their already huge fortunes during the profiteering of WWI. The ultra-rich tended to keep the true extent of their fortunes hidden, much as they do now, where it's estimated that less than 1% of the population owns 50% of the wealth in the USA.
Incidentally, if you're looking for a fascinating and little-known depression-era story, here you go.
http://www.republic-news.org/archive/98-repub/98_kropp.htm
http://www.squidoo.com/smedleybutler?utm_campaign=direct-discovery&utm_medium=sidebar&utm_source=Bob_Druwing