Your pistons have corrosion on them which prevent your being-able to push them into the caliper to load your new pads.
I guarantee I can get them to move. The traditional way to get them moving is to use compressed air into the caliper hose hole (the threaded hole in the caliper where the hose attaches) while using something between your old pads to keep the calipers' pistons from moving so-far that one pops-out but the other doesn't. I usually use a square-shank screwdriver in-between the pads and then blast the compressed air into the hose threaded hole on the caliper body. A wide rubber tip on your air tool will help to ensure your air enters the caliper.
This will usually work to get both pistons loose so you can remove them and then clean the corrosion off the surfaces of the sides of the piston and the caliper body. As I said, often one will move, but one won't. More compressed air, while limiting their movement via the tool between the pads, allowing some movement but not to where one which is now free comes-out of its bore before the other does.
If one is still not free, this will do the trick. Use a grease gun. Yes, a grease gun. You have to install a screw into the caliper threaded hole where the hose attaches. You don't need to turn it down tight, there are enough threads that you can just run it down to where it makes light contact with the taper at the bottom of the hole. Do NOT tighten it! Use some teflon tape on the bolt to help seal the bolt in the threads. All you are doing is using the bolt as a plug.
Now, attach your grease gun to the brake bleeder while ensuring the bleeder is open, and start filling the space behind the pistons with grease. THe stuck piston will pop loose. I have never been defeated by a piston using this method. Of course, now you have to clean-out all traces of the grease to be-able to reassemble the caliper and pistons. I usually use mineral spirits and a parts brush to ensure all traces of grease are gone, and then a spray can of brake cleaner solvent to remove any trace of the mineral spirits. Yes, you have to split the caliper open, don't lose the o-ring for the passage between the caliper halves.
I normally will use a wire wheel on my bench grinder to remove the piston corrosion. If after doing this you find the piston has any pitting on the surface where the piston makes-contact with the square rubber o-ring in the caliper body, replace the piston. If you don't, your piston/caliper will eventually leak. This will ruin your brake pads.
To clean the crevices of the caliper, I use a Dremel tool. They have steel or brass bristle brushes in different shapes. I use a round one for cleaning the caliper groove of all-traces of corrosion, and a cup shape to clean the bottom of the piston hole of the caliper. Again, mineral spirits and then brake cleaner. Be sure to wear eye protection, and nitrile gloves will help save your skin.
If there is any pitting from corrosion on either the pistons or the caliper, my recommendation is to replace the affected component. Therre are guys on-here all the time selling stock calipers, and you should be able to find one in better shape, cheaply. Hopefully when you overhaul it you find it doesn't have the same pitting your did. You can buy new pistons, or a new caliper but I don't think the caliper is going to be cheap. I believe one of the front calipers can be used in the rear position, I forget which one but another member will chime-in.
Some people will say that you only need to replace a component with corrosion if the corrosion is where the square rubber o-ring is making contact w/either the piston or the square slot in the caliper half. Given the function of what you're working on, is this really someplace you want to 'save a few bucks?'
For re-assembly, use a bit of brake fluid on the rubber o-ring sealing the pistons and caliper body. You should be-able to move the pistons in & out w/only finger pressure, easily. Coat the between caliper halves small o-ring w/brake fluid, and ensure it's centered in its niche before re-connecting the caliper halves. Snug the screws evenly and torque to spec according to the shop manual.
As I said, if the compressed air doesn't do it, the grease gun will.
