How do I get my iPhone and iPad to automatically search changes of IP addresses with WiFi extenders
Your devices (iPad, iPod) are not disconnecting from the first AP and connecting to the extender AP because the signal is still too good for it to disconnect from.

One of the best ways I have found to create a much more reliable wireless infrastructure is to turn down the transmission power of the WAP.  

In basic terms, this lowers the distance that a good signal will get to your device meaning your device will begin looking for a new WAP sooner.  The downside to this is that you will need more extenders.

The other way is to invest in "Enterprise grade" WAPs that have "handoff" built into the controller - this allows you to specify what the threshold is before the WAP "kicks off" the client and forces it to to search for another WAP.