CV Axle will NOT come out.

Sounds horrendous. Hopefully the shop can fix it without too much cost

 

I had to pull the axles to replace my transmission a few years ago. I remember there being very little to pry on and was very difficult to pry evenly to release the circlip. I don't remember much sliding of the end of the axle before that clip released, but I could be mistaken.

I like to get better leverage when I do stuff like this. One trick that has worked for me in the past is to put a reasonable quality hose clamp around the fat part of the axle by the transmission and make it good and tight. The screw part of the hose clamp makes a pretty darn good place to pry without messing with the ends of the axle. Better yet, use two hose clamps and you can position them 180 degrees apart to a good place to evenly pop out the axle. Be prepared to waste a clamp or two, but they should be cheap.

The axle seal wasn't bad to remove or replace. Only catch I found was they specified it had to be pressed in just beyond the edge of the axle casing. I got past that with an ABS plumbing connector from the home center and a washer made from copper wire.

All that said, your description of the axle moving freely but getting stuck seems odd to me. From what I recall, there was very little play at the end of the axle. More if you grab the shaft I think, but that's because of normal play in a CV joint

 

Just to be clear, I put the hose clamp around the black (non-rubber) part of the axle shown above. There are some ridges that can attempt to use, but they are so shallow that they are worthless. Probably made for a Toyota shop tool.
I don't think you should be able to see any of the shiny silver or brass parts of the axle shaft inside the transmission until that circlip has released. You also shouldn't be able to get at the oil seal in the transmission until the circlip has released. I don't think you really damage that seal until you take out the axle and somehow get part of the splined shaft to pull on the seal. I replaced mine because the scrap yard jammed plugs into the seal after they removed the transmission.

 

Yes, it can be very hard to apply pressure evenly to pry that inner CV joint out of the trans. Plus, you're usually lying on your back or belly with arms extended so you can't optimize the force you apply. Once force is applied evenly, the joint pops out and you wonder how it possibly could have been so hard.

There are a number of Youtube videos of techniques to pull a stubborn axle. One guy uses an OTC slide hammer with CV removal tool from Autozone. Another builds a similar tool from bar stock and an electrical junction box he has cut into a C shape. A third uses a length of chain and a slide hammer. The consistent theme seems to be to get out from under the car into a position where you can deliver force evenly. Also, impact force (from a slide hammer, say) is easier to apply evenly than prying force.

 

I would stake it and not give it much thought. I personally think it coming loose is unlikely but it takes a few minutes and I assume you have the tools