Looks like a good plan. Personally would prefer to have divided the 2 days (1 to CT and 1 to Venice) and done Verona as a day trip from Venice instead of staying there 2 nights.
Great decision to move the cooking day plan from Rome to Florence, smaller city and less to see than in Rome.
You definitely want to book ahead the Vatican museum online for a pre-arranged time booking, this saves literally hours online.
Not doing this in advance would be a major mistake unless you plan on only going to St. Peter's.
Borghese Museum is one where showing up is not an option, you need to decide in advance if you want to go there and buy in advance.
Also in Rome the Collesseum line is bad BUT assuming things have not changed rather than buy that in advance, you can visit Palatine Hill first which will likely have a small line. The ticket to Palatine Hill also includes the Roman Forum and Collesseum. So buy the ticket at the place with the shortest line and then you can enter the other 2 without a long wait other than security. I believe the one ticket gives entrance to all 3 sites and is valid for 2 days so you don't even need to fit them all into the same day, it takes a good portion of the day to visit these 3.
For Florence I would look into the city pass options for avoiding lines there depending on how many sites you want to visit there. If you don't want to buy that, The Uffizi Gallery is the one there you don't want to just show up at, same as the Vatican so book that if not getting a pass.
Venice I am not sure but there may be a site or two there where advance tickets would save you time.
Expect to spend a good amount of money for tickets to sites in all places either bought in advance or as a walk up.
