Does the Tywin that gives two gold at "the beginning of the Marshaling Phase" receive his gold BEFORE or AFTER Shadows? In other words, can I use Tywin's gold to bring a card out of shadows during the Shadow Step in the Marshaling Phase?

From the Shadows Rule Sheet:

"At the beginning of the any phase, a card that is in Shadows can come out of Shadows and into play at the discretion of the player controlling the card. (...) This happens before any other “beginning of the phase” effects occur."

So Shadows comes before Tywin gets gold for the phase. You cannot use the gold Tywin picks up at the beginning of Marshalling to bring a card out of Shadows during that same Marshalling phase. You can, of course, use any gold left on Tywin from the previous round to being cards out of Shadows, though.