What's funny here is RDU is a city I use often to get cheap flights. Many times DTW-RDU-ATL-LAS or DTW-RDU-ATL-MYR is cheaper than non stops. In your case FLL is served twice daily via Spirit and Delta will match fares most times. DTW-FLL 1 way can usually be had for $59 E, $79 economy and $179 FCM.