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I am so sorry to read about your difficulties.
There is a indeed a giant loophole. If your daughter were in the military you would have indeed been allowed to take the FMLA to take care of her. Currently, the FMLA only covers children but not adult children unless the adult children are in the military. I did not actually realize this giant loophole until you asked the question and I had to go and doublecheck it! It would have seemed to a casual observer and any reasonable person that you should be able to take FMLA to take care of your ailing child whether a minor or an adult child. Your child is your family member.
Regrettably, the denial of your request for family leave under the FMLA is compliant with the Act.
You may need to bring this to the attention of your Congressional Delegation to see if they can come up with an Amendment. However, in this current political climate and very dysfunctional Congress, I doubt anything can be done at this time.
I am sorry that I do not have better news for you.
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Thank you for your cooperation.