Sounds like the spindle is seized into either the bearings or the brake drum plate...or both. If you have time on your side, start soaking the brake back-plate area where the spindle passes through with something like Plusgas or parrafin. Don't worry too much about contaminating the brake shoes as they're dirt cheap to replace and if things havn't been apart for ages will most likely need doing anyway. After a week or so of doing this, try again using a suitable sized drift and a hammer to tap out the spindle, avoid damaging the threads if possible. Once it starts moving, tap it back again and get more Plusgas in there and work it back and fore a couple of times then it should come out eventually. Keep at it, it'll come in the end!
Just going for a short ride on my bike....