Praise be to Allah.
Firstly, may Allaah reward you with good for following the guidance of the Messenger of Allaah (peace and blessings of Allaah be upon him) and for calling your family to do likewise.
Secondly, shaving the beard is haraam, and letting it grow is obligatory, as you know. Obedience to the Creator takes precedence over obedience to any created being, even the closest of relatives. There can be no obedience to any created being if it involves disobedience to the Creator, and obedience to any other created being should only be with regard to what is good (ma’roof). What you describe of your father being angry and upset because you are letting your beard grow is only because he loves you and is afraid that what has happened to others may happen to you too. But what happened to others was, in most cases, because of provocation on their part, not just because they let their beards grow; it also happened to some of those who shave their beards. You must be steadfast in your adherence to the truth, and continue to let your beard grow in obedience to Allaah and in order to earn His pleasure, even if His creatures are angry. You must also avoid the sources of trouble, and put your trust in Allaah, hoping that He will provide a way out for you. Allaah says (interpretation of the meanings): “… And whosoever fears Allaah and keeps his duty to Him, He will make a way for him to get out (from every difficulty). And He will provide him from (sources) he never could imagine. And whosoever puts his trust in Allaah, then He will suffice him. Verily, Allaah will accomplish His purpose. Indeed, Allaah has set a measure for all things” [al-Talaaq 65:2-3] and, “…and whosoever fears Allaah and keeps his duty to Him, He will make his matter easy for him. That is the Command of Allaah, which He has sent down to you, and whosoever fears Allaah and keeps his duty to Him, He will remit his sins from him and will enlarge his reward.” [al-Talaaq 65:5].
We advise you to honour and respect your parents, and to explain to them with all good manners and politeness why you cannot do their bidding in this case.