I am sorry for your loss.
If your sister would also like to study, she could apply for a student visa; if she is qualified for an H-1B visa, you could assist her in finding potential employers.
Should you need to relocate to your native country for the assistance of family at this difficult time, you can apply for a reentry permit which will allow you to stay for up to 2 years without a problem associated with your GC. Be sure to apply before you leave the US if you think that an extended visit might be possible since it can only be obtained while you are physically in the US.
I know you are likely overwhelmed at this time. I would mention some of the things you need to be sure to do promptly in case you have not started taking care of the details that are so difficult to address soon after the death of a loved one. Be sure that you seek the Social Security survivor benefits that you and your child are likely due as well as benefits from his employer; for example, it is essential that you elect COBRA coverage within a specific time frame for continued health insurance. See if the university can provide additional assistance based on your new family status if finances for your education are an issue; you should speak directly with a high level person in the financial aid office. As you may have already determined, many legal issues arise from a death. Please seek legal assistance from an estate attorney specialist before leaving the country if you choose to do so to avoid missing any of the benefits to which you are entitled.
Best of luck to you both.
