You won't have any problems travelling via SR 528 (Beachline) East to I95 South, to Sebastian (Exit 156, SR 512). Take SR 512 East and make a right on SR 510 and go to the end where it intersects with A1A. Turn right at A1A and the resort is on the left. You'll pass within a couple miles of our house.
There is some construction on I95 but it's bearable and we go through it all the time. There are the usual unavoidable stoppages from accidents.
If you really want to avoid the construction area you would have to go south on Narcoossee Rd, which is just east of the airport, and turn onto SR 192 East to Melbourne where you can pick up I95 at exit 180. It's the same mileage but adds about 20 to 30 minutes to the trip. Very relaxing compared to going via SR 528 and I95 the whole way.
Chuck
Note - just re-read OP's msg and realized that they were travelling on the 21st. I'll leave this msg in case it may help someone else.