Can this be fixed at home?

In answer to your original question, "can it be done",,

If you put the wheel back on,, and gently rock it back and forth,, while pulling on the pinion,, the pinion should come back into place so you can get the yoke back on.. if not,, you'll find a wrench, although inconvenient, will work to get the axle nuts off..

hope it helps

Yea, I realize I can get the axle flange nuts off with a wrench. What I am really concerned about is getting the axle unstuck out of the third member now. Hopefully it will pop out with a little effort.
Can I tighten the pinion nut up and fix my problem or does it need to be serviced by the shop again?! Thanks again for the advice!