Breaking the nut free on the end of the shaft is not easy.  Click here to see a Yoke Holder (shown in the axle rebuild section) that will hold the shaft still.  Or  you can lock the front hubs, shift into 4-Low, transmission in 1st, and have a helper stand on the brake pedals.  By applying the brakes, the front axle is held stationary and therefore the transfer case output shaft, too.  Without a helper on the brakes, the axles and engine turn as you try to break the nut free.  You can also apply the parking brake, but that is no help if pulling the drum because of an inoperative parking brake.  If you can beg, borrow or steal an impact gun it will spin the nut off easily with no need for a holder.

The parking brake drum is a lot easier to remove from the shaft with a little shopmade tool.  Your first thought might be to use a three-jaw puller like this first picture, but I don't recommend it.  This is a spare brake drum I had in my pile of parts and it had cracks in it.  The cracks appear to have been from the previous use of a puller like this:

Instead, a short piece of angle iron comes to the rescue.  The length is not critical, but 4" worked well.  The drum has a concave rear face so the angle iron cannot be much longer than that.  Drill a pair of 3/8" holes on 3.125" centers to catch a diagonal pair of bolts on the companion flange.  The holes can be a bit bigger than 3/8" if desired for an easy fit.  Since the shaft protrudes slightly, as you bolt the piece of angle iron in place, it will pull the companion flange and brake drum free.  After breaking free, you may need to loosen the bolts and stack some washers against the shaft to take another bite:

If you'd really like to get fancy, drill and tap a hole in the middle like this:

You might find the drum-to-flange bolts spinning when you try to remove the nuts.  Here is a view inside the drum showing the lip that holds the bolt heads stationary.  It is pretty common to find the lip chewed up next to the bolt heads, allowing them to spin as you loosen the nuts.  If the nuts only make a few turns before the bolts spin, apply pressure under the nuts with a thin crowbar.  This will help keep the bolt heads fully seated.  You could also push the nut towards the shaft centerline while turning.  This will help jam the bolt head towards the lip:

After you have the drum removed, click here to read about replacing the shaft seal.