I have always used the day-by-day containers and never (so far!) had any problem. The only exception is a very strong (narcotic) drug for severe pain. I've never had to use it, but wouldn't go anywhere without it! I would make sure, if your Father takes any of those, that they are carried in the original bottle.
Or, if you don't want to take the chance, take the meds to your pharmacist and ask if they will make up smaller bottles for you.
I also take a few day's worth of extras, just in case we get delayed.
I carry a list of all my prescriptions and what they are for all the time. If something happens away from home it will be very helpful to have.
As LisaK said, always carry your meds in your carry-on bag. Your checked luggage may be delayed or (very rarely) not show up at all.
Have a great cruise!