When and Should I file a wrongful termination case?

Your union should treat you like any other union member. If they recommend you agree to the last chance agreement then they should assure you that every union member who is insubordinate is recommended the same option.   You can retain private counsel at your expense. More employees do this because if you go to arbitration and lose the chances of a successful appeal are not great.   Everyone today has a target on their backs. Duty of Loyalty, Faithless Servant, and Master Servant Doctrines are all good common law in New Yotk whether someone wants to admit that or not. And although your child is rightfully important for you there is no duty to accommodate your child, just you. You can request FMLA but once that is gone there is no possible extension of that like there might be if it was your own disability.   In your particular case you should pay a decent amount of money ( sometimes you get what you pay for) to an attorney who limits their practice to labor and employment law to spend a few hours with you and truly and honestly tell you the reality and choices you are facing. 25 years or 5 years on the job the union should treat everyone the same. Lots of employees would probably jump hoops to get a union job today and then never raise their voice no matter how much a supervisor yells. Your supervisor might have no union protection. Which means if you don't do exactly as instructed the supervisor loses their job with no warning and no questions asked.   It's brutal out there when you have absolutely no union and get absolutely no second chance as it looks like you might be getting. Another option is to pay a private labor and employment lawyer to review that last chance agreement and confirm what you might already know. Is there hidden discrimination not related to your child going on? Sometimes employees are sure of discrimination and after a few hours a skilled lawyer sees a completely different and unrelated discrimination which the employee never would have discovered. Not always, but paying for a consult does sometimes bring up hidden prejudices which are illegal and the claim the employee wanted to pursue is not the one which can potentially be proven. Almost never are discrimination claims easily proven no matter what they are.