Can a resource card be used more than once in a turn when allowed to build more than one structure?
The consensus opinion, based on asking the games' creators how situations such as these were intended to be resolved (see this BGG thread), is that you should treat Babylon's "play last card of each age" power as, in effect, a 7th and separate turn.  If you do, then naturally you would be able to use your resources once per build, not have to divide them between the last two cards.

I think this is definitely the way to go, just for pragmatic reasons: Babylon's power seems pretty poor if you have to pay for your last two cards in an Age with one set of resources.  It's hard enough to buy one card with the resources available in the final stages of the game - buying two at once would be an almost impossible feat!