The shoes swivel in the middle, are held static by the adjuster (a folcrum of sorts) and are pushed out by the wheel cylinder.
You can often push both shoes together and collapse the wheel cylinder a little. Giving you some more room. Double check your springs, make sure something isn't in the wrong hole.
After reassembling everything, don't count on the first stop (first time you try the brakes) to do much. Crap no brakes... It often takes a few cycles of operation and maybe some adjustment to get it right. And/or new brake shoes and pads, often have a shiny coating that actually doesn't work very well for stopping. But usually gets worn off in short order. I lightly sand mine before installation.
There is really no reason not to file some of the outside ridge off the drums, with a half round file. A little less material in this area, can make getting the drims on much easier. And a little filing after each show replacement, helps avoid the ridge getting so high you can't get the drums off again in the future, without major sweat.
When the drum doesn't align with the studs, slap the side of the drum with your palm, it will usually shift, without too much force.
