I'm fairly certain that you can only view the main palace after the Secret Itineraries Tour and that you can't re-enter. However, if you do need a lunch break, there's a cafe in the basement of the palace. I didn't eat there, but it looked decent.
There is plenty of time to do the entire tour of the Doge's Palace and then St. Mark's. There is no tour of St. Mark's that I'm aware of (although Rick Steves' free iPod audio tour is great). You can book admission in advance (for free), but the basilica itself doesn't take much time. Once inside, however, there are other sections (can't reserve in advance and you do have to pay): the Golden Altarpiece, Treasury, and the Museum. We didn't go to these, but I can't imagine that they take a lot of time either.
We did the 11:35 Secret Itineraries Tour, spent some extra time in the Palace, grabbed some lunch, checked out St. Mark's Square a bit and went into the Basilica at our reserved time of 3:15. We didn't want to be rushed, but it turns out that we could have reserved an earlier slot than 3:15 without any rushing.