IOS – How to verify which wireless access point the iOS device is using

I'm pretty sure this is not possible to do on vanilla iOS, perhaps with a jailbreak.

However, your solution of running two separate WiFi networks is generally not what you want. It is much more common to extend one WiFi network (i.e. a single SSID) with multiple routers. Devices should then automatically switch to the access point with the stronger signal.

You can check this question which describes how to setup two APs for the same network (i.e. a single SSID).

You can not tell from the iPhone directly (as of iOS version 7 native). You should be able to tell via the wireless router your connected to in it's logging functions, WiFi client list or some similar mechanism within the router. I can't provide you an exact process as every router is different. This answer assumes you do not want to JailBreak your iPhone. If you are not adverse to doing so there may be an app in the Cydia app store that will show more meaningful information with regard to WiFi frequency information.

You can however detect what cell tower frequency your phone uses by using Field Test mode. This will special mode allows users to find out a range of information about the phone’s connection to the network. In particular, the information displayed in the Field Test mode allows users to discover exactly which tower their phone is connecting to and which frequency band (WiFi) the signals are being sent on.

To access this mode:

• Access the iPhone's Field Test mode by typing *3001#12345#* in the phone’s keypad and press dial. This will bring up the Field Test menu.
• Select the “Cell Information” menu option to display a summary of all nearby towers. The “RX” code displays the signal strength of each tower. These RX values are dBm signal strength readings, where lower values means strong signal (so -60 signifies stronger signal than -80). The towers are listed by signal strength, and the top tower is usually the tower your phone is connecting to.
• Selecting the first tower will take you to a further menu that displays more specific information. The “Freq” value shows the frequency block that the network is using. If the Freq number is between 128 and 251, the tower is using the 850 MHz Cellular band. If the Freq number is between 512 and 810, the tower is using the 1900MHz PCS band.