name of this part?

The rod on the left is the centerlink.
The one that has the ball end and the stud that goes through the hole is called the TIE ROD END:D (The right inner tie rod end to be specific.)

I have kids that I'm envolved with this evening so sorry if I lag here and there on response.

If you dont need to save thoes parts, hit it harder on the end of the threaded bolt part.
If you need to save the parts, take it to a shop and have them disassemble it for you.