This will be our 5th cruise in April, and we have booked all of our shore excursions through private companies....except the very first cruise, we booked them all thru Carnival. And from that first cruise experience, we found that for the money we spent, and the large groups of people that you are packed in with....we now like to find them on our own and have never been dissapointed!! I understand your worrying about getting back to the ship on time, just plan very well and give yourself additional time. In Roatan last year, we waited 45 minutes past the time we were supposed to leave the port for a family of 4 who came running up the dock 45 minutes after the ship was supposed to be gone. I don't believe that this family of 4 was on a Carnival Excursion, and they held the ship just because they were on a Carnival excursion. The ship knows who is on the ship and who is off the ship because each passenger has an ID card that they swipe when getting off and getting back on. We have always planned on getting back on the ship 45 min.- an hour before it is due to sail.
As far as renting a vehicle for the day...have never done that, can't help you there.
In Grand Cayman, our private catamaran pulled up beside one of the tours that was from Carnival, and the people were packed on those boats like sardines....our private catamaran only held 30 people, and we all had room to lay down and catch some sun rays on our way out to the sandbar to see the stingrays., plus we also did 2 additional stops to snorkel on our way back. I have actually done this same excursion thru Island Marketing on the buccaneer stingray excursion 2 times, 2 years in a row!
Our cab ride to West Bay Beach was with another couple that was also looking for a cab to the same beach. The cab driver was amazing...he made many stops along the way to show us his beautiful island. We did not feel unsafe at any point. Our cab driver had us back to the ship by 4:00, and the ship left @ 6:00.
If you want to be safe, and ease your mind since this is your first cruise(?).....go with the carnival excursions, then next time you cruise book on your own, then you will have the comparison of both ways.
I will tell you that the only place were we felt a little unsafe was a private tour in Jamaica (Ocho-Rios)., that was I am sure due to the excursion we chose however. But, since that cruise I pick my itineraries to avoid Jamaica, there was nothing about Jamaica that I would care to go back and see.
Also, I wanted to tell you that Island Marketing is very reputable...did you have a chance to check out their website? They offer excursions in many ports. They also will credit you if by some chance your ship does not port on that specific day. We didn't make it to Costa maya last year, and had an excursion booked thru them...I emailed them when we got home, and they had already credited my CC. They are aware when a cruise ship does not make it into port.
Hope all of this mumbo-jumbo helps