You need to use a special set of probes called Kelvin Contacts. You are going to have problems with the instrumentation because the relay contact resistance is probably lower than any other part of your measuring circuit.
The special probes have one set of wires where you put a constant current. Then the other set of wires is used to measure the voltage. You may have to solder the wires to the relay.
12-bit is not enough.
For 4.095V at 12-bit you have 1mV resolution and this will be not near resolution which you may need to measure such low resistance. I think you should look at at least 16-bit A/D.
DrWhoF