Here is how a typical home network is/should be setup.  DSL line goes into WAN port of router > Router provides WIFI to wireless devices and wired devices plug into the LAN ports of the router > Router provides addressing to each connected device via DHCP.

Now to "complicate" it.  There can only be on DHCP provider on a network or conflicts will bring the network to a halt.  If you need to more wired devices than your router can provide you can plug a network switch into one of the LAN ports to give you more ports.  If you need additional access points you can use a true access point or an extra router.  If you use the router you must disable the DHCP on it and also only use the LAN ports on it and NOT the WAN port (unless your trying to create separate firewalled subnets).

In your situation plug the ethernet cable that goes to your shop into a LAN port on your router in your house.  In the shop put another router and plug the ethernet cable into a LAN port as well.  You will most likely have to manually assign an IP address to the shop router and also disable the DHCP on it.  Give the wireless SSID the same name as you have in the house with the same encryption password and type of security.  If you do this your computer/internet network will be the same in your shop as in the house.