you must be a citizen first before ever travelling back home if you feel safe.As an asylee or with a green card,you are still a citizen of your country and the reason they do not want you to go back home is because if something happens to you they wont be responsible since you are still a citizen of your COP ,SO the only time they can assist you is if you are a citizen f the USA ,because every citizen has the right to travel where ever he wants without restriction.I will advice you not to go back if you really dont want to get in to trouble at the port of entry.None the less you can still get back in even if you go back to COP but just be sure to provide enough evidence why you went back and why it was necessary ,also when ever you travel uscis keeps track of all your destinations and when you will apply for citizenship ,if they see that you went back to COP ,you will probably have problems there too ,but it can still be resolved but I wont advice you to take that risk because all of these things is luck ,if you have bad luck you will have troubles if you have good luck everything will be fine but I dont advice you to go back.Just pray God your relative gets better.Good luck