@edgarblythe,
Most likely, the old shoes have worn a groove in the drum, and the ridge at the outside of the drum is binding when you try to remove it. Don't know your model, but there should be a tiny access port on the axle that will let you back off the adjustment enough to let the drum clear the shoes. If this is the situation, you are also going to have the drums turned.
Oh, wait. This was a question for mechanics. I used to be a bookkeeper, though.