Maybe JB weld some threaded rod to the center of the broken axle shaft, stick a thick washer on it and then a nut at the end of the rod to keep the washer in place and then use a slide hammer to pop it loose. Either that or have someone weld it to it, but not sure if all that heat would be good for the seals around it.
Technically it only has to hold enough to get the c-clip on the end of the axle to pop free from the trans and out it comes. I'd think some JB would hold enough for that.
Also, not sure how good of luck you'd have drilling into the anyway as it's probably some super hard steel.
The C-clip is attached to the end that is still in the trans. When you get your new CV axle there should be a new clip on the trans. end already. No need to remove the old one from the broken piece.
Yes, it will pop loose from the trans and then when you install the new axle give it a shove inward towards the trans. and it will click into place.
Ohh.. But according to Facebook, you said it was your dumbass lsx boyfriend that did this...
#Girlproblems
... Well anyways, just smack the output shaft from the other side and it should pop the diff out as well. Just make sure to unbolt the diff cover.