Probably the steel plate has rusted and jammed at the edges.
You could heat the steel pad backing plate with a torch until it's very hot, waiting a minute, and then pressing an ice sube against the plate. The sudden change in size as it cools down might break it free, the aluminum caliper part will stay hot and "large" longer than the steel plate. Heat might damage the caliper paint, though.
The backing plates usually have a dimple on centre so that the pad can float to the right angel for the disc. Laying the caliper half on something solid then whacking the plate down around the edges will want to make it rock, freeing the stuck edges maybe.
Soaking the whole thing in Coke for a day or so should loosen any rust, the weak phosphoric acid attacks rust but shouldn't bother the alloy caliper or paint.