While I haven't tried mounting a drive through a router (my previous office had no problems with computers on a wireless router printing to printers on the wired LAN the router had been plugged into), you should be able to use Map Network Drive and specify the laptop by IP address from the computer. For instance
\\192.168.137.1\folder should work. This will only work from the "inside" of the router to the "outside" since most consumer class routers also act as firewalls.
Your setup would be ideal if you had a switch (or if this was wireless, an Access Point without a router) rather than a router, this would allow the other computers to appear on the same network as the laptop. You can fake it by attaching the laptop to the "inside" of the router rather than the "internet" side and disabling the router's DHCP service. Computers connecting to the router should then get an IP in the 192.168.137.x network and the 192.168.137.1 gateway from ICS directly.
If this is a wireless router, be warned: if try this with your laptop connected to your router wirelessly, you'll have half the wireless bandwidth because each packet will have to be sent twice: from the computer to the router then the router to the laptop. If your wireless router has LAN ports for the inside network, that would avoid this issue.