There is no right to form a public sector union in the first amendment. Teachers can associate with whomever they like, but the government can enthusiastically reject their demands and fire them if they want for doing it too. That's what free association means
Correct, and if they do, the entire union can go on strike, which is the whole point of a union. What you seem to want is to make it a crime for one worker to refuse to work if another worker is treated unfairly. You can 'ban' employees from unionizing, but that means having to fire literally everyone who is willing to join the union. That's essentially what you are advocating. It would be a battle of nerves, with poor families suffering the most. And that is of course what conservatives really want. American Conservatism has become little more than a psycopathic hatred of the poor, with no opportunity to exploit, insult or injure them neglected.
Also, keep in mind that union members are also voters, and active ones at that. You can't ban people from voting against politicians who try to prevent them from organizing. But you are fine with big corporations lobbying lawmakers, aren't you? But when actual voters do it, it is somehow undemocratic?
A labor union is a corporation. This means a labor union is created by the same mechanism by which a legal corporation is formed.
Neither are gifts from God or an act of nature.
A labor union exists and must operate within the legal code which defined it and made it possible. It's not a matter of rights. Incorporation is one of the privileges of living under a system of government which has enough power and wherewithal to create such laws and enforce them.