^^^^
What does the garage that you trust think of the people who 'did the alignment'?
I would firstly tell the alignment company that you are very dissatisfied and why (can you cancel your payment?)...
Tell the garage you trust that there appears to be a problem with their ball joint installation and tell them what the alignment company found...
Get the trusted garage to put it right (within their original charges)...
Go back to the alignment people and ask them to do the job properly and you'll be happy to pay them properly.
Be polite but firm and ask all those concerned to please understand your point of view. Tell us what happens please