Going the other way
My earlier statement that clients connected to the first router won’t be able to access any clients attached to the second router for file and printer sharing actually isn’t entirely true. By using the second router’s DMZ (or exposed computer) function you can actually share in this direction, but for only one second router client at a time.
All you need to do is put the IP address of the computer you want to share in DMZ, then use the WAN IP address of the router when you go to access the computer. You don’t have to worry about weakening security for the computer that you put in DMZ, since it’s already protected by the first router’s firewall. But if you’re really paranoid, you can open just TCP and UDP ports 137, 138, and 139 to the IP address of the computer that you want to access instead of putting it in DMZ.