Kroil
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a rust penetrant that becomes indispensable after using it for awhile. Not sure how you removed half the axle, on mine it was all one piece. Typically, the carrier bearing gets stuck in the cast iron housing. That's where you spray Kroil and let it soak in. Recently twisted the head off an old bolt on the Toyota truck water pump. After seveal days of soaking, was able to remove the stud with vice grips. Also that pesky lower flare nut fitting on the fuel filter came off instantly after a couple days soaking with Kroil. Should help your axle carrier bearing release also - and that's all that holds the axle, once the bearing is loose, the axle will slip right out.