How do I hook up a Wireless Router to a second Powerline Adapter in Living Room to have a stronger Wireless Network Connection

You don't want a wireless router connected to the second powerline adaptor, you need a wireless access point.
Some routers can be put into access point mode, some can be re-flashed to give them that capability (see openwrt.org).

Hi,
I explored the wireless access point method to extend wifi range in my previous house, a particular room which I used as my office (2 bars) and the room above the garage wouldn't pick it up at all. I got a tp-link wireless access point which was configured to relay the signal and boost it. I had mixed success with this, it used to drop out occasionally, my wireless printer wouldnt work off this at all and created a bit of lag while surfing/gaming. After using this for about 4 or 5 months I decided to instead of using the access point, replace the router with a 3 aerial 300mbs Tp-Link router and replaced the routers standard aerials which were detachable (3 x 3dbi) with 3 x 8dbi aerials (purchasable from sites like amazon, they are a little on the long side but do the job), the wifi card on my pc I replaced with a tp link 300mbs with 3 detachable aerials and replaced them also with 3 x 8dbi aerials. The signal in my office room went from the previous 2 bars to 4/5bars and worked brilliantly, the room above the garage went from no signal to 3/4 bars.

I found it was better to replace the router and this removed the lag problem and meant that I did not need additional kit. This may not be the best solution for you, but perhaps replacing the router or even the aerials on your existing router if they can be unscrewed with 8dbi aerials may improve things for you. I believe the massive gain for me came with a combination of the changes, but just replacing the router and aerials on the router would give you some gain.

Also note routers with more aerials are able to perform better in areas where interference is a problem or signal ghosting is a problem. If your current router is a standard free from your ISP router then changing the router to a 3 aerial variant (make sure you buy one with detachable aerials) may be all you need to do and then if you still want to improve further replace the router aerials and then if you still want to improve further the pc/laptop wireless cards and aerials.

Also moving the position of your router away from things like old style tv's, fans, etc can improve performance slightly.