How can I isolate an indoor water pipe to prevent freezing?
I agree with the comment in that its surprising the copper pipe would conduct enough heat to freeze the downstream pipe, are you sure there's not a draft or something like that?

Your idea to isolate the pipe seems relatively sound though.  You would likely want to use PEX instead of PVC. PEX normally requires a special tool to crimp the connectors, so I would recommend using a SharkBite push-in coupling fitting to connect the PEX to the copper and vise versa as these don't require any special tools to install.


From http://www.sharkbite.com/product/couplings/


  SharkBite is the Push-Fit connection system that is really taking hold. It’s the easiest way to join copper, CPVC or PEX pipe in any combination with no soldering, clamps, unions or glue. Just insert the pipe and the stainless steel teeth bite down and grip tight, while a specially formulated O-ring compresses to create a perfect seal.


I don't have any affiliation with SharkBite, they are just a well known brand of push-in fittings.  Your local store might have other brands too