I want to connect some sensors to the input pins on the 3rd XBee (the one without an Arduino).
OK. Go right ahead.
From my other XBee which is on an Arduino, I want to read the values of the input pins on the 3rd XBee.
It doesn't work that way. The 3rd XBee needs to read the values of the pins, and broadcast them. One or the other of the other XBees receives the packets sent by the 3rd XBee and needs to decode them to determine what the 3rd XBee found the pin states to be.
This is almost entirely a configure-the-XBees-correctly issue.
I'd strongly recommend that you acquire "Wireless Sensor Networks" by Rob Faludi. It is an excellent resource for using XBees in AT or API mode, and configuring them to read I/O pins, etc.
The book applies specifically to Series 2 radios, but most of the examples and exercises work equally well with Series 1 radios.