Last week Trenitalia posted an update on the Civitavecchia service for 2022.
The timing doesn't work for most cruise passengers unless their cruise ends in Rome but here it is.
There is one morning CE train departing Civitavecchia at 9:07, arriving to Roma S. Pietro at 10:00 and Roma Ostiense at 10:10.
There is one afternoon run departing Roma Ostiense at 16:30 (4:30 PM), stopping at Roma S. Pietro at 16:43 (4:43 PM) and arriving to Civitavecchia at 17:20 (5:2
Your hotel is just steps from the #8 tram line, which you can take to the Trastevere station to get the train to Civitavecchia.
The regional train isn't horribly crowded going toward Civitavecchia in mid-day, so if you're aiming to be at the cruise port between noon - 2 PM you should be fine.
The train from Civitavecchia is direct, but it makes a lot of stops along the way. The fare is 4,60 euro. For example, there's a train at 12:27 that arrives to Civitavecchia at 13: