As the others have said, it's a matter of doing the math and considering not just which attractions you can fit in but how often you'll be taking public transit. Also be aware that while the card allows for ticket-line skipping, it doesn't eliminate queues for security checks.
DO make advance reservations for the Vatican Museums: the Easter season is a very busy time for that one!! I'd consider booking one of the three-hour museum/basilica combo tours offered on the website? Tours can access the basilica DIRECTLY from an inside stairway at the back of the Sistine (in the museums) so it eliminates standing in another security queue. At the end of your tour, you're free to wander about church at your leisure.
Depending on the ages of your children, 3 hours straight of art/artifacts/architecture may be the limit of their tolerance anyway? You can reserve a tour slot here:
http://biglietteriamusei.vatican.va/musei/tickets/do?action=booking&codiceTipoVisita=74&step=2
It's only possible to book 2 months ahead of the current date, and I'd expect Good Friday mass to restrict visiting hours to the basilica on that day.