Arduino RFID Multiplexer Antennas
You are not going to be able to "copy" the signal of the mux to the reader via the arduino board. If you connect the antenna to the arduino analog input through the multiplexer, the signal will be converted by the ADC, and the best you could do later is convert it back with a DAC, losing a lot of signal integrity. This scheme is far from optimal, what you should do is connect the antennas directly to the reader through the mux, and use the arduino to select which is connected.

A multiplexer connects a certain input to an output according to a selector signal



In this 8:1 mux, the s0, s1 and s2 signals select which of the 8 inputs is connected to the output. So, in your case, the inputs of the mux should be the atennas, and the output should go to the input of the reader. With your arduino you should control the select signal. So, by giving values to the select signal, you can select which antenna connects to the reader.

You should analyze the impact of the multiplexer on the connection between the antenna and the reader, too.