Wifi At a pub. ?

hiya Peeps

You know how it is, a little bit of knowledge is an easy way to tie yourself
up in knots ..

Thats where I am right now :-)

lets see if i can explain my dilema.

I have a shop next to a pub, the distance between the shop and the pub is around 50 meters but I want to connect to the pub's 'N' wifi ( I have permission )
Walking from the pub towards the shop the signal drops out around half way across the car park separating the two buildings.

Now I bought a TP-Link Wireless-N300 ADSL Modem Router/AP to install in the shop but it is too far away to receive the pubs Belkin signal even though the TP link transmits twice as far as the belkin.

As a very last resort I may be able to install the TP-link in the PUB but I need the LAN input in the shop and not just be able to pick up the wifi. so have just bought a TP-Link TL-WA830RE Wireless-N300 Range Extender, I am hoping this will take the Belkin signal as far as the shop.

If it does I want the AP in the shop so I can connect a card swipe machine to the LAN port to be able to process card payments.

So its like this Pub phone line>Belkin 'N' router/ wifi .......TPlink range extender------Shop>TpLink Wireless-N300 ADSL router/AP

is this possible to set up without plugging the second TP-Link AP into a wired LAN ? or am i dreaming ?

Regards
Rich