Adjust park brake because the caliper is sticking

There is no adjustment at the caliper for the parking brake, it is integral to the caliper, there is a gear within the caliper piston which turns it outward when you step on the park brake pedal, that is why you must use the piston tool to rotate the piston inward when you replace the pads. The adjustment is at the parking brake cable under the drivers door next to the frame, loosen or tighten there, give it a healthy dose of anti-seize compound, it'll always work for you. If your parking brake is not releasing correctly, the problem is within the cable itself, they don't last forever, or the caliper piston itself is sticking, you said you replaced the caliper though, unless there's an issue with the new one.

How did you get the piston to retract? There wouldn't be enough clearance for the new pads to fit, you wouldn't be able to put the caliper back over the disc. If you used c-clamp or some type of tool used to push the piston back, such as the tool used for the front calipers, you most likely will break the gears within the rear pistons. On a new or rebuilt calipoer the piston may or may not already be in the retracted position.

There's a little tool you can buy expressly for the rear caliper pistons, normally around 10 bucks or so, it fits on a 3 8 rachet and allows you to retract the piston, make sure when you do, you leave the notches (2) in the 12 and 6 positions so the pins on the pads will fit in.