Electronic – Shunt Current measurement isolation problem

You're looking for an isolation amplifier. These are great if you're looking for a monolithic solution that is easy to integrate, but might not be cost-optimized. Some even provide a little isolated (HV-side) power via an internal DC/DC converter to run scaling op-amps, etc.

I've had good luck with the Burr Brown ISO series of isolation amplifiers (acquired by TI a few years back). The ISO122 is a general use product, and the ISO124 has higher accuracy.

Analog Devices also makes a few general purpose isolation amps.

Just be aware that some sort of modulation is required to move the signal across the isolation barrier within an isolation amplifier. Some do it inductively, some optically. Either way, plan on a little ripple on the output signal. The specs usually do a good job of outlining the limitations.

Yes, in general relays provide isolation between the switch contacts and the coil. You need to check the data sheet of the relay to check the maximum voltage it can isolate. For instance, this omron relay: http://www.farnell.com/datasheets/77391.pdf?_ga=1.209377874.1513769717.1469465786 has a dielectric strength rated to withstand "5000 V between coil and contacts for 1 minute".

You also need to check the contact ratings to make sure they can handle 120 VAC at the current you are using.

There do exist signal relays designed for switching small amplitude signals like audio or RF. These are relatively uncommon now as they are much more expensive than solid state switches, so you aren't likely to use one by accident. Signal relays may or may not have the isolation you want, but almost certainly don't have contacts that can handle power switching applications. Pretty much any relay with 120 VAC contacts should be able to handle isolation for this type of application.

However, there is more to it than your relay. The rest of your wiring needs to be safe as well. This is particularly a concern with PCB mounted relays -- you need to make sure the PCB tracks and pads have sufficient clearance so that you can't get arcing from the HV to LV sides if there is a power line surge, and the board needs to be properly assembled without oversized solder bulges and with any flux reside cleaned, and maybe a conformal coating. It is better but more expensive and inconvenient to use a relay with screw terminals which can be located physically away from your low voltage electronics. You still need to make sure that your wiring has mains rated insulation, and all possible touch points are shielded.

This is all fairly easy power electronics stuff if you know what you are doing, but a small mistake can kill you. If you are not sure about doing this, it is much safer to use something that has all the power wiring done for you. For instance, this "power-tail": https://www.sparkfun.com/products/10747 which allows you to switch power loads with a low voltage signal, and provides all the isolation for you.