Budgeting Time in Rome

My wife and I will be travelling to Rome in late March and I was wondering how much time to budget for certain sites. We’ll be in Rome for three full days before moving on to Florence, and were thinking of the following:

Day 1: Vatican Museums, Sistine Chapel, St Peters, Castel Sant’Angelo, finish the day wandering around Trastevere (including Santa Maria)

Day 2: Colosseum, Forum, Capitoline Hill, Pantheon, maybe Mamertine Prison; I was budgeting the whole day for this…too much? Also, can you enter at the Pantheon and go “backwards” finishing at the Colosseum?

Day 3: Mixed bag of other places we’d like to see…St Clement Basilica, Capuchin Crypt, Spanish Steps, Borghese Gallery, etc.

Our hotel is near Trevi fountain, so we’ll see that and Piazza di Pietra while walking around.

Edit: also, since we'll be in Rome for three full days, should we look into the Omnia Card?

Do you think we’re trying to fit too much into our itinerary? Am I overestimating how long people generally spend at these sites (thinking of the Colosseum to Pantheon leg here)?

Any advise is appreciated!