Ok, so I have been thinking about your setup here, it's a little confusing with the way you have drawn the diagrams but all the information is there :)
Your wireless connection ( now pick my bad drawing!!) is:
node (a) <------> (node no-name) <--------> node (B)
The initial config had the Internet connection at node (no-name) and worked Ok for all connected clients.
The desired configuration is to move Internet connection to node (a) and use 192.168.0.0 as the segment address, with the Address of the router being 192.168.0.50
From your diagram it is unclear how you have the AP, PC and Router connected at node (a), The AP has a single network port, so do you have:
The AP, router and PC all connected via a hub or switch or
The Router has multiple interfaces with the AP on one and the PC on the other or
Is the PC dual homed and the router is in one port and the AP in the other?
in pictures:
CODE
node (a) AP |-----+ H
PC |-------------+ U
DSL router |------+ B
or
node (a) AP |------------| (eth0) DSL router (eth1) |--------| PC
or
node (a) AP |-----------| (eth0) PC (eth1) |-----------| DSL router
My guess is that your lack of Internet connectivity is probably related to not having IP forwarding on the PC rather than anything to do with the wireless network set up. If you can ping between the machines then it means that in the local network you have connectivity, having the default route set to the (assumed dual homed) PC would get packets to that machine but if it is not configured to forward the packets then they just get quietly dropped.