Here's another idea-
Do the Walks of Italy Fri night Vatican tour
https://www.walksofitaly.com/vatican-tours/vatican-night-tour/
Get to St Peter's by 4:30/5ish- if you are visiting there as well? And if you can stay awake thru about 10 pm! It is going to be "hotter than Dutch love" as my grandma used to say. See the Pantheon, nearby churches, P Navonna, Trevi, Campo de' Foiri etc- the first half of RS Heart of Rome Walk as soon as you are checked in to hotel- go back to your hotel to refresh and cool off- then walk over to St. Peter's and visit on your own- have a quick dinner nearby then do the Vatican night tour.
That leaves the entire next day open so you can do a morning Colosseum tour and rest of your sights that 2nd afternoon.
If you do book with Walks of Italy I am pretty sure they offer a discount for multiple tours and possibly a Rick Steves discount as well- email them and ask.
We have actually found we do better if we do take a very quick nap on arrival- if we can get into our room and we have been lucky every time- set an alarm- 75-90 min, change/shower if you need to then out for the evening. It just works best for us. Everyone is different.