Rome Miles and Miles

Just walking off the ship and taking a car service is very luxurious. The train is far less expensive, and takes you to a station for the Vatican, then you then must walk around the Vatican to get to the Museum entrance.
. A tour of the Vatican Museum is an excellent idea especially if you think you won't return. I would suggest, since I think you want convenience, that you check into the Cruisecritic Roll calls ( create a sign in, then look for the cruise line'roll call' and your departure date, then look for posts for the specific ports) for your departure, and see if anyone is organizing a small group for what you want to do. That may be a very effective compromise, traveling with perhaps 12-16 people on a semiprivate tour. I have had great success with the roll calls and tours.
Remember the distance between the port and Rome is far, and traffic builds up- this a reason for the train IF you are comfortable with that.
I was completely underwhelmed by the Colosseum, whereas I have visited the Forum and Palatine Hill etc several times. Have been to Rome several times, and visited it twice as a day trip from Civitavecchia. Use Rick's suggested restaurants near the Vatican for lunch- trust me on that.

We traveled in Asia and had private tours. I did an search of cruise ship,tours of the port we were in.

We booked private tours, for roughly the same price as tours organized by the cruise ship company. So I would search for cruise ship tours to the Vatican. Likely you can find a private tour. If the tour company uses trains the do that as they know the best options.

I suspect the tour company can accommodate your needs.

Will the private car and driver get you a "skip the line" entry to the Vatican Museum? If not, that could be a very frustrating day for you.

Will the private car and driver get you a "skip the line" entry to the
Vatican Museum? If not, that could be a very frustrating day for you.

That is an excellent point, especially as you mention the service you've looking at "does not include museum tickets". If you want to get into the Vatican Museums without wasting a LOT of time in a long queue, you need to book your tickets in advance for a specified time slot. Two hours is also going to allow you very little time to navigate the vast amount of ground the museums cover. If that's all the time you have, I would book a tour through the Vatican website (see first one one the list) to make the most of it.

http://mv.vatican.va/3_EN/pages/z-Info/MV_Info_Servizi_Visite.html

To reserve, scroll down to the bottom of the page and click on "To book a guided tour click here."

Are you interested in doing this on your own? If so, I will post some recommendations. If not, hire the driver. Civit.... is over an hour from Rome so that adds to your costs.