Definitely don't beat the caliper back on. It should slip on with just a little jiggling and moving around to get the pads over the lip at the disk edge.
Did you make absolutely certain you did NOT activate the parking brake or that you did NOT touch the rear brake lever?
Doing either of those with the caliper off the disk will cause the pistons to be pushed out and make it impossible to get the caliper back on without spreading the pads.
When I replaced the rear tire, and the front tire for that matter, and took the caliper off the disk I inserted a paint stick wrapped in some card stock (a bit of junk mail) to keep the space between the pads.
If the caliper will not fit over the thickness of the disk you can use a few putty knifes (putty spatulas) between the pads and pry them apart. Do this slowly. I use a thin pry bar between the putty knives to do this if needed.
This is also assuming the short spacer is in place in the right way (should fit up against the bearing race on that side).
Here is the document I wrote up and posted in a thread in this sub forum for doing the rear wheel remove and replace, including replacing the tire on the rim and balancing with Dyna Beads.
https://docs.google.com/document/d/1za6fOBjIUv364F9nwP9_mNgzOEtrC0ThA4GcpAJxHgE/edit?usp=sharing