Problems amplifying mV potential differences
Your amplifier looks good in theory. Most likely the 741 and the low input signal is the culprit. The µA741 is a very old OpAmp. It was a good chip 40 years ago. These days you should only use them (if at all) for educational purposes. (They are really robust little chips that can take a lot of abuse, that's why they are popular in school and university).

Anyway, back on topic: I've designed something that may work for you:

 

U1 is your non inverting amplifier. I picked some reasonable resistors which give a gain of around 256. 

U2 is a peak detector. The amplified positive half-cycles get rectified and charge capacitor C1 up to the maximum voltage seen at the non-inverting OpAmp input. After a few mains cycles you will see a constant voltage here.

Now you can sample this voltage from the Output pin. If you want to do a new measurement, just put a 0.1 second high pulse (3.3 or 5V) onto the reset input. This will let the transistor conduct and discharges the capacitor for the next measurement.

You need a bipolar power supply (not shown). +/- 5V is fine.

If you have to go shopping for a OpAmp, try to get a precision OpAmp which has enough output compliance. E.g. you'll want something that can drive the output  close to the positive supply as possible. The TL081 suggested by others will not do this. With a +/- 5V supply it will only go up to 2V. Ideally you'll want a rail-to-rail OpAmp, but you may get away with a cheap LM358 as well (goes up to 3.5V on a +/- 5V supply).

One last thing: You may want to put some more windings on your inductor. 2 to 4 mV is not much and close to the noise generated by the OpAmps themselves. A healthy input voltage would be in the range of 20 to 40 mV. Adjust the resistors around U1 accordingly.