I am able to turn the piston, but it will not screw into the caliper. Am I doing something wrong, or is this something that a pro needs to look at.

You need to push the piston with a little force while turning it clockwise. Also, make sure the master cylinder isn't full. The master cylinder needs to be slightly empty to allow the fluid to return from the caliper. If the master cylinder is full it creates a hydrolock situation.

if you plan on doing your rear brakes more than once go get yourself an actuated caliper tool. handy as **** and most come with adapters for many cars. wont cost you too much if you know where to look. most of the cars i get at work wont go in by hand.