Hello and thank you for your post. I am a master certified GM tech. If I can help you solve this today then I will, lets begin
the axle you bought might just be bad or wrong?
that stub shaft has to be removed using a special tool that you install in the groove where the c-clip sits, you pop it out using a slide hammer, then install new c-clips and pop it into the new axle and then install the axle
if the stub shaft stayed in the trans, leave it be
the new axle just pops in like the old one
there is a normalamount of lateral play, any more than normal will cause a leak
so if the axle seal isn't leaking, you are probably normal
there is no replaceable bearing in there without disassembling the entire trans and replacing the differential (final drive unit)
does the vibration go away when you let off the gas (instantly) if yes then one of the axles are binding (inner cv joint not sliding in and out properly)
otherwise I would look elsewhere for the vibration unless it wasn't there with the old axles but is there with the new ones
there was an updated lower control arm bushing and steering rack pressure dampener spring released for the 2000 and 2001 L-series cars that would help reduce vibrations
here is the info on the bulletin for the vibration (and it covers 2000-2005 saturns, thats new, used to go just to 2001
Some customers may comment regarding a steering wheel shake or vibration felt when driving vehicle at highway speeds. This condition is most noticeable on smooth road surfaces at vehicle speeds above 65 mph (105 km/h).
This condition may be caused by vehicle sensitivity to out-of-balance tire/wheel assemblies.
Balance all four tire/wheel assemblies and evaluate. (Regardless of VIN.)
Replace steering gear preload adjuster spring. (On vehicles built before and including VIN 2Y525531.)
Replace front lower control arm rear bushings. (On vehicles built before and including VIN YY697118.)
Caution MAKE SURE VEHICLE IS PROPERLY SUPPORTED AND SQUARELY POSITIONED ON HOIST. TO HELP AVOID PERSONAL INJURY, PROVIDE ADDITIONAL SUPPORT TO OPPOSITE END OF VEHICLE THAT COMPONENTS ARE REMOVED FROM.
Tighten Tighten Wheel Bolts (Initial Torque) to 63 N·m (46 ft-lbs).
Tighten Tighten Wheel Bolts (Final Torque) to 125 N·m (92 ft-lbs).
here, I'll just attach the entire thing...
hope this helps