Suggest that you unplug the Express and temporarily move it to the same room where the AirPort Extreme is located.
Power up the Express and let it run a full minute or two. Then, push in the reset button on the Express and hold it in for 7-8 seconds, then release.
Allow 40-45 seconds for the Express to restart and display a slow, blinking amber light.
I am assuming that you are using AirPort Utility for the iPad since you mention iOS 5.1 in your post. If not, download and install App Store - AirPort Utility
Tap Settings on the iPad home screen, then tap Wi-Fi
AirPort Express should appear under the heading of Set up an AirPort Base Station
Tap AirPort Express, and AirPort Utility will take a 25-30 seconds or two to examine your network and then declare that the Express will be setup to extend the AirPort Extreme.
Tap Next in the upper right hand corner of the window and allow a minute or two for AirPort Utility to configure the Express and wait for it to restart again with its new settings.
When AirPort Utility tells you that the AirPort Express is now extending the AirPort Extreme, the Express will display a green light.
Now, move the AirPort Express to a location that is about half way between the AirPort Extreme and the general area that needs more wireless coverage, plug it in and allow 40-45 seconds for it to start up and display a green light.
You should be in business.