I am sorry to hear about your Father's condition. I see no need to worry. First of all, I believe you will receive an I-797 to extend the expiration date of your Green card when you submit the I-90 for renewal. Secondly, even if you had only an expired 10 year Green Card with you outside the US, airlines are allowed to board you to return to the US with an expired 10 year card.
Just renew your Green Card when the time comes....and take care of your Father. The Green Card will not be an issue. Good luck.