Go to 192.168.0.2 > interfaces [UPLINKEDINTERFACE]... and put in a DNS/GATEWAY ( which more than likely would be 192.168.0.1 for both )
fyi you "pinged an ipaddress of a website" which does not test DNS.... so you had a gateway presumably... just no dns.... next time ping a name too, as there is a difference....
P.S> Thanks for the diagram.... it really helps....
For Everyone with the same problem, this is what you have to do:
when you are in the OpenWrt menu: go to Interfaces and then to LAN
for your first router the IPv4 address and the IPv4 gateway must be the same
for your second router you have to set the ip of your first router as the ip of the IPv4 gateway and the custom DNS server
You probably have to reboot both Routers after this (do this if you can't access any sites afterwards) Good Luck!