I think you have explained it the way I thought it might happen. Seems that last paragraph is the key to understanding how an objection to the Electors of Alabama who voted for Obama would hold up the whole process.
So at that point would the Vice-President order Obama to produce proof in the form of his valt BC? Or would it be the DNC?
It is pretty clear that the Vice President presides over the proceedings. He is responsible for certifying the EC vote as valid. The objection to the votes for B. HO. arise from the question of his meeting the natural born citizen requirement. The first logical step in making that determination is obvious, produce the original birth certificate. Depending on what information it contains there could be other objections.
The Electors of Alabama would almost surely vote unanimously for McCain, since McCain won the state in the election. Assuming the electoral votes are presented in alphabetical order by state, all the electors of the next three states - Alaska, Arizona, and Arkansas, likely voted for McCain as well. It would be the electoral votes from California for Obama that should prompt the objection.
Incidentally, according to what I've heard, at least one Democratic elector appearing on the Dem slate in California filed before the election has been dead for seven years! That should prompt another objection on another ground from any congressman or senator concerned about the integrity of the process.