Most shops use a hydraulic press against the splined shaft end. An 8" thick home made spacer should be used on the other end to barely clear the axle flange. Pressing directly on the stock brake rotor surface will usually crack them. My spacer catches the sloping edge of the brake rotor center, NOT the braking surface of the rotor. You can make the pressing-out easier by individually pressing each wheel stud towards the carrier; even though the studs cannot be removed yet, it reduces the force necessary to move the axle. And if it seems to take more than a small 10-ton press delivers, you likely have something wrong with your fixture.
Force needed to push the axle out depends on the assembly- I've seen some rear uprights in which the axles FELL OUT of the bearings while others were super-tight. The bearing mfgrs specify 0.0005-0.0008" interference fit between bearings and axle shaft. This takes a 4-place 0-2" micrometer to check and few ever do. Once the thing is disassembled, re-flatten the steel bearing retainer on the outside of the carrier; high press force will bend it into a cone shape so on reassembly, the new parts will be loose even at the required 450-ft-lbs of torque on the axle nut. Don't worry about stripping the threads- that size thread fails at 1200 ft-lbs according to the SAE. And if you can't get the axle nut loose because someone Lock-tited it on, simply cut it off and use a new nut (available from all the vendors). Ideally, OEM split-nuts shouldn't be re-used anyway.