Axle won’t pop into transmission

Are you certain the other "C" ring came out?
You can also inspect the trans to make sure there is nothing blocking the axel.
There shouldn't be, unless that ring broke.
If nothing is blocking the axel, then you have to force it in.
You might have to remove it, rotate it a little and try again.
You can try to hold it perfectly straight and tap it in with a larger hammer.
Put the axel nut on first though incase you mess up the threads.
Then you can file the threads and remove the nut.

 

Rather than tear up threads, you can also just install an old axle nut about 90% of the way as a thread protector. Preferably installed backwards so the heavy flange is facing outward. Beat the snot out of it if needed and then remove the nut. Threads should be fine.

 

Just ONCE it’d be cool, if one of the Shop Manuals (aka Repair Manual, sans Toyota) had a writer with a sense of humour, slipped an expression like that in, like an Easter egg.

And yeah, it IS a good tip.

 

When I fit an axle into the trans, I first use a little grease (or petroleum jelly) on the splines of the axle to keep the snap clip centered. It will want to drop down and get pinched by the receiver splines in the trans/ diff if it is too far off- very likely on a "new" axle. Then keep the inner joint centered and straight as possible while inserting. If possible, pull & strap the knuckle out of the way, get the axle straight (with the old nut on the end of the outer joint threads). Push the axle in to bottom out the inner joint then pound on the nut with a BFH. If it doesn't go after a couple hits, pull the inner joint out slightly, rotate 180*, push it in an hit it some more. If it's still a problem, take it out, check the clip for damage- sometimes I have better luck reusing the old clip. Once it's fully seated, give the inner joint a little tug to make sure it stays locked in place.

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You got the axel OUT???? Didn't you want to put in IN????
It should NOT flop around. If it is, maybe you don't have the correct axel.
Measure the spin diameter and see if it matched the original one.
Once the axel is in, there should be virtually NO play. Only from the cv joint.
I that what you mean?

The oil seal only keeps the oil from coming out, and dirt out.
The

 

Okay, didn't see where you had done that....