Couple of good shots with a dead blow hammer should release the tie rod.
That carrier bearing can be problematic at best. Some heat on the outer
carrier housing may be required

I have a gut feeling that if the tie rod end are rusted and are too
tight, you could mar the stud after accomplishing your task.

Tie rods are easy.  You just need a hammer.  How you use the hammer is not
obvious.  You don't pound on the threaded end!  You bang on the end of the
arm that recieves the threaded end.  Keep the nut on the end of the tie rod
incase you miss your target with the hammer.  A long time ago a mechanic
friend taught me this trick, and I have used it many times.
-----------------
Alex

As for removing ball joints, I have had very good luck loosening the
nut (do not remove the nut - you'll need it to protect the threads).
Being careful not to damage the grease seal, install a pickle fork AND
a screw-type ball joint puller.  Put pressure on the pickle fork while
tightening the joint puller.

I have released the most stubborn ball joints with this method without
needing a buddy to help and without breaking anything (on me or the
car).

Also, keeping the nut loosely attached to the ball joint will keep the
arm from flying if you have a sudden release.