When MSW says that Coccopalmerio must have been "happily influenced by the Orthodox way of treating second unions," because "he makes the case that admission to the sacraments requires not only a consciousness of the irregularity, but a desire to change it even while admitting the situation cannot be changed" . . . he's confusing second marriage ceremonies in the Orthodox Church with second marriages. 

Second marriage ceremonies in the OC are low-key and penitential. But like every other misdeed, you repent and move on. You certainly are not expected to spend the rest of your second marriage apologizing for your first. That would be unfair to everyone you have become enmeshed with--new spouse, children, extended family, and so forth. Once you are married, there is no barrier to the sacraments--in fact, it is expected that you will partake of the sacraments wholeheartedly. This is a very important distinction.