When we took our then-10yo daughter on her first visit to the Vatican Museums, we bought tickets in advance from the Vatican, so we didn't have to stand in line, then guided ourselves through using a number of books, including Rick Steves. That allowed us to spend more time on the sights that we liked more. The three of us really like art; we spent about 1/2 day there, with most time spent in the museums, then the Sistine chapel, and least time of all in the basilica.
Husband and I had taken the Vatican Museums' two-hour tour (it ended at the entrance to the Sistine Chapel) on a previous trip, and felt that it spent time on things that we didn't care about, and rushed us through other parts of the museum, and didn't go into the Pinocoteca portion at all.
Whether your 13 and 9 year olds will like it depends on them and their personalities.