Someone on the Bethesda board figured out the "cards don't go into your deck" problem:
The cards are supposed to be deleted from inventory and added to your deck when you acquire them. And this works if you take them from a body or a container. Possibly also if you take them from the ground. But it doesn't work if you buy them.
One assumes this will be fixed in a future patch. In the meantime, just add the cards to a container and then take them back. I can verify that they then show up in your Caravan deck the next time you play, on the "select your deck" screen. You still need to scroll over to them and add them to your active deck.