To make 3 devices that have a very general idea of their distance from each other via RF signals.
Simplified list of issues.
#1 I do not know what all the pins on the transceivers do exactly, and I can't find a page where someone has tried to interface those with an Arduino. #2 I do not know which lines need voltage changes.
All one can tell from that spec sheet is that the radio is an SPI Slave device. Fortunately I was able to find a reference to the internal chip: EM198810. Unfortunately I can't find a full datasheet for that chip. I found many copies of a PRELIMINARY datasheet which has a chart of what values to put in what registers if you are using a 12MHz crystal, but it doesn't say what the data means or what other registers might exist.
Unless you can find a register that has a signal strength value I don't think you will get much in the way of distance measurements.
#1 How many bad packets is one device receiving from the other? #2 Sending one ping from one device to another then returning it and reading the return time.
This does not need critical measurements, if I can tell 50' from 25' I'll be happy.