There was a severe thunderstorm warning that covered Port Canaveral that expired at 4:15pm that day.
I haven't found exact times Indy left (scheduled for 4pm), but here's a Carnival ship leaving a few minutes before the storm hit. Weather didn't look overly imposing.
It shouldn't be a problem at all to update the cruise reservation. Name changes on flights are harder, but if it's not past final payment, should be easy for Air2Sea to do.
People can be sympathetic about the death of a person unknown to them and be concerned about how they are going to get home.
Humans are fully capable of emotional multi-tasking.
This isn't always true. Storms don't always crawl in with plenty of lead time. They can pop up out of sunny skies in minutes. That's likely what happened here and why they pushed off when they did.