Ummmm, I don't think it was the CA that broke the axle.

I have a couple of tools that were designed just for the job that you have. They are basically a length of heavy fencing wire, [or thin rod] with a spiral cone at each end. That makes 4 ends in all with different sized cones for different sized axles. The idea is to slide the right size end into the axle housing untill the wound cone reaches the axle & you turn it as if you were screwing it onto the axle stub, which in fact is what you are doing. The fact that is is made of spring steel makes it all work & once you have got it on firmly, you simply pull it out.

In the old days, cars broke axles all the time & many garages [not service stations] actually carried a stock of popular ones, so this is the sort of place that might still have one of these axle remover tools, assuming that any older workshops still exist in your area.

While you have it jacked up, pull ther other axle & have a good look at it, particularly in the area of the splines. This act might just save you from a repeat performance shortly after returning the car to service.