Hi, OK, I think this is a very rushed day, especially seeing the Vatican museum in 1 hour, then getting. back to Roma Termini in time for a 4PM train. Do you have any leeway at the end of the day, in case you take a later train? (PS, just as I was posting and trying to figure out how to say, 'drop one of these' others said the same thing. Yes, please, drop one.)
I would look up all the taxi stands you will need, you can 'save' them on Google. Suggest you Google places to eat near the Colosseum to grab a pizza by the slice. Take some power bars along just in case?? Here are just a few places to grab a bite - https://colosseum.tours/information/page/best-food-on-the-go-near-the-colosseum-1593431881645.
12:30pm -1:30pm Express Tour of St. Peters Basilica - Going to assume that this is an actual St Peter's tour but is it a 'skip the line' tour? Everyone has to go through security to enter St. Peter's, so check with the tour about the wait.
1:30pm-2:30pm Break (Snack/Explore?) - I would head straight over to the Vatican museums, which is a 10-15 minute walk from St. Peter's & could you try to get those tickets changed to 2PM? It would give you a bit more time to get through the museum.
2:30pm Skip the Line Tickets for Vatican & Sistine Chapel (No Tour/Explore @ our own pace). Your pace will have to be quick, and it will be entirely crowd dependent.
4:00pm: Take Train back to Ship/Port - This is where I think you've underestimated the time needed.
Let's assume you get through the Vatican M in one hour, you then need to make your way back outside to the taxi stand to get back to Termini and find your train, board by 4PM. (I would allow AT LEAST 30 minutes for taxi trip, plus waiting in line for a taxi, plus finding the platform, so let's say 45 mintues to an hour, suggest you look up the taxi stand location so you can go straight there, & download the train appso you can buy tickets ahead of time on line.) I just looked at the time to cross Rome by taxi in the middle of the night, it says 15 minutes. Depending on what day of the week, it could take 45 minutes in rush hour traffic. Good luck!! Planning ahead will help!