Sitting in vomit?
I am not questioning anything that you are saying - I am happy to take your story at face value - and you have my sympathy for having endured such a miserable experience.
Your question is whether anyone knows of a law or rule that might govern such a situation. I do not and cannot help you there.
I am responding for one simple reason - your story is the kind of story that makes headlines. It is the kind of story that ends up on Yahoo headlines and Good Morning America. So while I am not challenging your account, I would suggest exercising caution to ensure that you do not let anyone influence you to exaggerate the details so that you are not later victimized again by the media.
I would suggest a letter to the airline asking if the procedures followed by ground staff and the flight crew were in accordance with airline policy. In other words, if this were to happen tomorriw to another mother with small children would the airline expect the same result. If they say yes - then the media will eat it ip. If they say no - then they are acknowledging a systemic failure and that they owe you something.