Extending a wireless network for stronger Wi-Fi signal?

Hi. I just bought a new Airport Express to solve a problem I've been having, but I don't think it's working. My base station is in the front of my house, but the signal from it is just barely able to reach the back yard. I have my stereo attached and speakers run to the yard for Airplay from my phone, but Airplay craps out sometimes due to connectivity issues (I guess, it's hard to troubleshoot.)

The base station was the old Airport Express, and I bought a new Airport Express to replace it, and set up the old one in the back yard-facing window to extend my wireless network (I chose Extend my wireless network).

However, what I noticed is that even though my phone has line-of-sight to the old Airport Express from the back yard, it remains connected to the base station, sometimes with one bar of signal. I haven't tested how well Airplay performs but it appears that my phone won't simply choose to connect to the strongest signal available but holds on to the first connection as long as it can, even if that means weaker signal.

Am I misunderstanding how this works, or is there an option that will enable me to strengthen my Wi-Fi signal when still marginally in range of the base station? Thanks!

 

How do I get the Airport Expresses to talk to each other in this configuration? I've tried this and I might as well have two independent Wi-Fi networks, neither sees the other, and only one has the resources I need (Internet, Airplay speakers).