I'm gonna be a contrarian here and say that a day trip to Pompeii is actually doable. The train from Rome to Naples is not two hours, more like an 65 minutes, from what I recall, and then if you take the express Circumvesuvina, you're at Pompeii 20 or so minutes after that. You just need to make sure it is the Express Train. The Rick Steves book spells out the process really well.
We did the day trip from Rome in July 2018. We made sure to book an early train to Naples [think 7 am hour]. We arrived to Pompeii at it's opening time and wandered around the ruins before meeting up with a guided tour from a local after lunch that we booked through Viator. It effectively meant we were double paying to get in but we really didn't care. It allowed us to see some stuff we knew we wouldn't get to on the guided tour.
We finished in the early afternoon, taking the train back to Naples, and then used the subway to get to the Archaeological Museum. I don't remember its closing time and we certainly didn't get to see everything but we really didn't want to. We went to the rooms with the art taken from Pompeii and a few other exhibits to "complete" the Pompeii experience. We were back to the train station to catch a 7 pm with plenty of time. We ate inside the train station. Wasn't awesome food but it was fine.
It was admittedly a long day but in my eyes, it was very worth it. And again, doable, with careful planning. Follow the Rick Steve instructions. If you do the Archaeological Museum, read the instructions in the book about which subway line to take. There's a Metro that runs directly to the Museum area and a one time ticket is only 2-3 Euro.
[I'd skip your companion's village if you truly want to allow enough time for Pompeii and a potential trip to the museum.]
EDIT: I'll say though that Rome has plenty to keep you occupied, if you say it's not worth it. We spent 8 days there [with the one day dedicated to Pompeii] and even with 7 full days in Rome, there was still additional things we could have done.