How to get the caliper to push in so the new brake pads fit around the rotor?

Try putting the old brake pad against the piston, open the brake bleed screw on that caliper and apply uniform force on the center of the pad/piston using a brake caliper piston retracting tool or adjustable pipe wrench. If it won't retract there is a problem with the caliper being partially seized requiring both calipers to be replaced as a pair.

use a big c clamp