Take FMLA leave.

FMLA leave and emen1). You can take FMLA leave, it is job-pretected by the labor law in the states, which will be able to give you up to 12 weeks leave without pay( still have your job!!!!!). Check this link;http://www.dol.gov/esa/whd/fmla/, so you won't challenge your GreenCard application.

2). Get a doctor's notice for your mom's disease( make translation and notarization for the documents) ,
then go to the USCIS local office with doctor's notice, your birth certification , pay 200$ and get a emergency AP there the same day.

I just went through this last month, all the best for your mom.