Sorry to hear ...
You got 2 options. First, get somebody to fax you that this is an emergency in emergency cases and try to obtain AP from local office. (Personnaly I did not hear that you can kick in the local office door and request AP).
Second option taken from USCIS website states :
"To request expedited processing, provide the reason(s) why you feel the case should be expedited. Be sure the request is supported by adequate, relevant documentation. State "EXPEDITED HANDLING REQUEST" in the heading of the letter and on the envelope." - this is could be done for seven reasons, only first one could be work related.
1.Severe financial loss to company or individual.
2.Extreme emergent situation.
3.Humanitarian situation.
4.Nonprofit status of requesting organization in furtherance of the cultural 5.and social interests of the United States.
6.Department of Defense or National Interest Situation (Note: Request must come from official United States Government entity and state that delay will be detrimental to our government.)
7.USCIS error.
Compelling interest of the USCIS.
My friend asked for expedited AP without no documented proof, just a letter that family member is not feeling good - one month passed, no AP....
Good luck.