You can still travel with your green card. Just let your local office know that you will be away, so they can schedule you for a later date.
This answer is for informational purposes only and should not be construed as legal advice.
Schedule an InfoPass.
Bring a letter from the doctor proving that she is seriously ill.
PROFESSOR OF IMMIGRATION LAW for over 10 years -- This blog posting is offered for informational purposes only. It does not constitute an attorney-client relationship. Also, keep in mind that this is an INTERNET BLOG. You should not rely on anything you read here to make decisions which impact on your life. Meet with an attorney, via Skype, or in person, to obtain competent personal and professional guidance.
Try to schedule an infopass and explain. I doubt it would help but you can try.
The information contained in this answer is provided for informational purposes only, and should not be construed as legal advice on any subject matter,not should it be viewed as establishing an attorney client relationship of any kind.