1989 Mazda 323 Stuck Axle

My sister-in-law has a 1989 Mazda 323 automatic transmission sedan with under 150,000 miles on it. It started "shaking" and "not driving right" so she stopped & called her brother & my father. My father came to where she was and could find nothing wrong. He started it up and drove it more than 30 miles to her normal repair shop without any "shaking", etc. - It drove perfectly fine. It was determined that the front driver side axle needed to be replaced and she told them to go ahead with the repair. Evidently, the axle was "stuck" (inner sleeve?) And they couldn't get it out to replace it. They said they used a slide hammer on it and when that didn't work, they drilled a hole (we think torched) to hook into and tried to pull it off/out with a truck. Nothing they did worked so they said the only thing that could be done was to replace the transmission (at big $$$). She told them to stop - don't do anything else, she'd take the car somewhere else. They left the car in pieces - transmission put in the trunk, etc. So it had to be towed but they made her pay $800.00 before they'd let her take it.

The mechanic at the 2nd shop (my father had it towed there) had absolutely no problem whatsoever removing and replacing the axle. He accessed and removed a retaining ring from the passenger side - easy, squeezy. He also had to reinstall the transmission while he/we hoped that it was still okay after the condition the 1st shop left it in. Well, it wasn't - gear box grinding up a storm so it was a goner.

We found a transmission for it and she's back on the road - all of the above is just explanation leading up to my question: Does anyone have or know of any documentation, etc. That tells or shows a mechanic, like our 2nd one (who's now our #1!), How to remove a stuck or difficult axle?

Even my mechanic (in a different city) knew how to do it when I described the problem. How do they know this when the 1st shop didn't? They claimed to have called a Mazda dealer and transmission shops, etc. And they all said the ONLY solution was to replace the transmission. Well, that IS what had to happen but only after THEY beat the crap out of it first! We're all convinced that the transmission would have been just fine if they hadn't damaged the gear box during their brute force attempts to remove the axle. It drove into their shop just fine without any slipping or any other indication of any problem with the transmission. I've already done a lot of Internet searching, etc. Myself including signing up for a week at eAutoRepair but I didn't find anything after hours of looking at that documentation. Any help will certainly be appreciated!

PS - What does DOJ stand for? I think the J stands for joint but I have no idea what the OJ stands for (not trying to make a funny). :) Sorry this is so long-winded but didn't know how else to approach this!