We've done it a bunch of times. I'd rather fly in and out of FLL than Miami any day. Smaller airport, less traffic, the car rental lines are shorter, etc. The drive to Miami is only about 15-20 minutes and since the construction finished they also fixed the exit so you you can go south out of the airport instead of going north up to the u turn. There's a gas station just before you get to the airport and a few roads south at A1A and Stirling there's an Ihop in case you are like me and crave a stack of pancakes after your flight, there's a Walgreens with attached liquor store across the street. Stirling takes you to the I95 to Miami. The overhead signs are massive so you can figure how not to to get on to the toll lanes.
Just for fun we stayed at Comfort Suites on 36th a few years back. We took the rental back and should have walked back to the hotel but we took the shuttle. All we could get for help was to go to the ground level and wait. No specific area just flag down the first shuttle you see and hope it's not full. I was with my son, we waited about 10 minutes and got lucky with a shuttle. Oddly enough we met a family going on the same Wonder cruise who had been waiting for an hour for the shuttle and they were told the same thing. Had it not been for the rental return we would have steered clear of the Miami airport.
Now if I can figure out how to bank enough money to buy a place at the Palms in Fort Lauderdale when I retire...