The text on Tywin is:
"You may spend gold tokens on Tywin Lannister as if they are in your gold pool."
So let's break that down:
- "You may spend..." When reading a card that says something like that, starting with the word "you," who does it apply to? When the word "you" or "your" appears on a card, the effect only applies to the controller of the card. "Characters you control get +1 STR" means characters controlled by the controller of that card. "You may initiate an additional INT challenge this round" means that the controller of the card can initiate the additional challenges. So this would mean that only Tywin's controller can spend the gold tokens that are on him.
- "...as if they are in your gold pool." When reading a phrase that says "as if," that thing is not actually true, you just pretend it is for a limited purpose. If you decide to have a party in April "as if" it were Halloween, people might wear costumes to the party, but you're going to get a lot of weird looks if you go around the neighborhood Trick-or-Treating. So, for the limited purpose of spending gold, you pretend the gold on Tywin is in your gold pool. For any other purpose (counting Dominance STR, Taxation. Dany's ability, figuring out Littlefinger's STR, etc.), it is not in your gold pool.