Melt butter in a large nonstick skillet over medium-high heat. Cook bananas in butter until they are browned and begin to soften, about 1 minute. Remove pan from heat; stir in rum, nutmeg and cinnamon. Use a long match or lighter to carefully ignite the liquid in the pan. Allow to burn for 15 to 30 seconds; if necessary, extinguish by placing lid on pan.
Continue to cook until sauce has reduced by half, 2 to 3 minutes. Stir in lime juice; cook for 1 additional minute.
Divide ice cream between 4 serving bowls. Top each with the warm bananas and rum sauce mixture. Drizzle each sundae with chocolate sauce, and top with whipped cream.