I have a bit of a problem with the general statement that aftermarket parts are junk. Not that they can't be, anything can be junk but as I do most of my own work and have for years I just have not found that to be true. I have used a fair amount of rebuilt axle shafts (at least a fair amount for a back yard mechanic) and have never had a problem with them. I have though when there were still Saturn Dealers and there are none any longer, had problems with over priced shoddy repairs done on mine that I had to pony up and re-do and eat the expense on. Or sit and have a serious discussion with the service writer why it was required that I spend $50.00 or so having windshield wipers replaced when the reason I was there was the sun roof was in a failure mode.
There is more than one engine mount to position the engine in a Saturn or any front wheel drive car. If there is enough movement going on to break a particular mount repetitively such as the transmission mount AND have an Axle half shaft pop out that is a lot of movement and an indicator that there is something else going on too. I would have to go look at mine to make sure I say this right but if my memory is correct the lower control arm function, that it the thing that serves as a lower control arm is also the front sway bar. An interesting concept of using parts, but that piece locates the lower ball joint which positions the steering knuckle. The steering knuckle has the bearing in it that supports the outer end of the half shaft and if the steering knuckle is moving around than I can see it pulling the half shaft out of the differential which is part of the transmission.
My point if any is there are a bunch of things that might be going on causing this problem and at the moment it sounds as if you have not located the real problem yet, but have been treating the symptoms of it. At the moment I would make an attempt to locate the rest of the engine mounts to see if any of the others are broken.