I had an 45 minute lay over in NC when my mom passed away, well the plane was delayed leaving Orlando, due to weather with the incoming plane
and I did miss my connection flight by minutes and NO that plane did not wait for any of us.
To top it off the connection flight was on the other side of the airport. Had to wait another 3 hrs for the next plane. Never ever again..
There is a hotel in Miami airport.. not the greatest, but not the worst and you are in the airport.
Another idea is fly one airline there and another one back; we did that before too.