Can I add the Airport express as a wireless access point?
Absolutely, if you connect from the other router to the WAN "O" port on the Express. (I am assuming you have a new AirPort Express with both WAN and LAN ports.
Configure the Express to create a wireless network, name the network, setup wireless security, a password and configure it in Bridge Mode.
I'm having set up problems. Install using iOS, can't get past the "power cycling" phase. I have 2 cable modems with battery backup, and have unplugged both the power supply and removed the battery from both for 5 minutes, and unplugged the above mentioned router. Powered up again the modems first, then the router to no avail.
Sorry, I do not have an iOS device handy to try to figure out what is going wrong. Having tried this in the past though, I have noticed that AirPort Utility for iOS tries to analyze the connection and then configure things automatically.
Unfortunately, it does not always choose the correct settings and then it is necessary to look for a way to manually configure things.
I may be able to use my wife's iPad later today. Please confirm that you are connecting an Ethernet cable from one of the LAN <-> ports on the router or switch to the WAN "O" port on the AirPort Express so that I can set things up exactly the same way here and work on a manual procedure for the configuration.