Hi spindoc -
If there is ANY way not to do Rome's #1 and #2 most visited attractions in one day, I'd make that effort? Both of them are going to be mobbed and you'd be spending your day - which is sadly looking like it may be the ONLY full day you have in Rome - smack in the middle of the hordes. This is the best way I know of to form a negative impression of the Eternal City!
So when, exactly, will you be in Rome? I'm seeing that it might be for just 2 nights on May 15th and 16th, coming from the Amalfi Coast with Pompeii along the way, or maybe the 17th as well (the Mille Miglia post). It makes a difference as the 17th is a Friday and offers an option for the Vatican Museums that's not available on the 15th/16th so could stretch your available sightseeing time.
Colosseum in the afternoon, since the latter has the cheaper
"combo-ticket" available for entry from 14:00 only?
That is outdated information. ALL pre-purchased tickets are now for a specific DAY and TIME, and they sell out very quickly so you need to jump on whatever times are still available. This is the ordinary-entrance ticket:
https://ecm.coopculture.it/index.php?option=com_snapp&view=products&catalogid=ADAE8874-AE4B-55B9-02FB-0167A81C0247&snappTemplate=template3&lang=en
I'd look at this option (entry plus 45-minute Colosseum tour; excellent price of € 19,00) too:
https://ecm.coopculture.it/index.php?option=com_snapp&view=event&id=E6A1B5B3-BFDA-AC94-6929-0161B2E3A0C0&catalogid=BDB46B8C-0C49-10F2-6036-0167A8502B26&lang=en
If sold out for your date(s), keep checking back. The website also states that "Pre-sales will be open every Monday at 9:00 am (ROME time) for Colosseum scheduled time entrance... for the following week according to the weekly availability." The ticket covers entry to the Palatine and Forum as well, and I think it would be a shame to miss them.
Sistine Chapel: it's at the furthest end of the Vatican Museums, a good 30-minute walk from the entrance when slowed by the crowds. Unless you book an early-entrance museum tour or a Friday night late opening ticket, I don't know as it matters when you go as it's going to be very, very busy ALL the time. A significant amount of posters have sworn that early-entrance tours, such as "Pristine Sistine" offered by Walks Of Italy, while pricey, were worth every euro to be able to see the chapel and parts of the museums before they got just nuts. There are a couple more quality companies which offer these tours as well so give a shout if interested.
Otherwise, you might try getting general-entry tickets for the earliest time slot and making a beeline for the Sistine. The museum's own ticketing website is here
http://www.museivaticani.va/content/museivaticani/en/visita-i-musei/scegli-la-visita/visitatori-singoli.html
This is the least-expensive, general-entry ticket:
https://biglietteriamusei.vatican.va/musei/tickets/do?action=gototipovisitapertag&tag=museibigliettiingresso&weblang=EN
For instance, does RS's tip for using the Sistine Chapel exit
directly to St. Peter's ....
That exit is reserved for tour groups so the ability of individuals to use it is up to the whim of the guards on any given day. While it's possible you'll be able to get through, it's not a given
We will have visited Pompeii the previous morning.
if you're doing Pompeii on your way from the AC on the 15th, you likely won't be settled into your Rome hotel until mid afternoon or later: allow 3 hours or more for the scavi (it's vast) + a couple more for the transfer process.