Do you think it's going toward the Cayman's?
Definitely. The question is at what strength.
The NHC has it approaching hurricane strength during that period, but not as more than a mild Category 1 hurricane. But there's no way this misses the Caymans.
This map shows Ernesto's center predicted to be near there at 2:00 AM Monday. I hope for your daughter's sake that they are wrong.