The weather will be warm but changeable. April is still possible to have 40 degree days, even in the keys.
I wouldn't leave the rain gear home. Most likely you'll encounter no more than short duration T Storms, but all day soakers are still a possibilty. It's the wet season.

The only real negative with your time table will be the crowds. April is Spring break time. Though the serious college crowds like to hang further north there will be plenty of overflow down to the Keys. Add in elementry school kids on break, the peak RV season, and the Keys can get kinda crazy in April. Not a deal killer for me, but just so you know. Don't expect to roll up and get a room at the inn without a reservation.