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I'm very sorry to hear about your situation. It's unfortunate when employers are unwilling to be even a little bit accommodating here. It's unethical, immoral, and illogical. But unfortunately it's not illegal. Alabama is an "at will" employment state. At-will employment means that without a contract, you have no contractual or other right to employment with the company. The company is entitled to fire you for any reason: a good reason, a poor reason, or no reason at all--as long as the company does not fire you for an illegal reason (race, gender, age, religion, etc...). But it extends beyond firing, to hiring, promotions, demotions, wage cuts and raises, disciplinary actions, and even scheduling. Unless you can show that this was done in violation of a contract, union agreement, or a clear violation of an unambiguous and binding clause against the employer, or that it was done because of some minority status (age, race, gender, religion, disability) that you have, then they do have this discretion.
Now your employer can't fire you because you have a child. But your employer can say that you can't leave during your work hours, etc... and that's entirely up to them. Again, I agree with you that it's unfair that they're not more accommodating, and I wish that they would be. But it's not illegal. It's still in the discretion of the employer.
I know this is probably not what you wanted to hear, but it is the law. I hope that clears things up anyway. If you have any other questions, please let me know. If not, and you have not yet, please rate my answer AND press the "submit" button, if applicable. Please note that I don't get any credit for the time and effort that I spent on this answer unless and until you rate it positively (good or better). Thank you, ***** ***** luck to you!