You have to be very careful when you type in numbers.
0.5 to 3 ohms is what mastermind meant to type.
OK, so is the Arduino running from 3V? That's fine. Using 3V also to supply current through the 470 ohm resistor means the voltage is scaled down, too. 19mV at 3 ohms will result in about 2V at the output of the second Op Amp stage.
A clarification on the word "amps": in this context, he means "amplifier".
You use two Op Amps because generally you don't want to try and get a voltage gain of 100 in one stage. It is simple enough to use two Op Amp stages.
The TL081 will not work unless you supply it with at least +5V -and- -5V. It is not rail-to-rail, nor is it well suited to a single supply low voltage.
http://www.ti.com/lit/ds/snosbw6a/snosbw6a.pdf
The ubiquitous LM324 is not well suited, as the output can only go to a voltage 1.5V below the supply voltage. You should pick out a RRIO Op Amp, something rated to run down to 2.5V single supply voltage. It doesn't have to be fast.