What is the ruling on shaving the beard in this case?

If shaving the beard poses a real threat to your life, then it is permissible to shave it, and obeying your father in this case is an act of obedience in what is right and good.

However, if there is no legitimate Shar’i justification for it, then there is no obedience to him, and you should seek help from virtuous individuals to advise him.

Some scholars have permitted trimming the beard, lightening it, or taking what exceeds a fistful. If this pleases him and removes the hardship from you, then there is no harm in it, as it is permissible to take advantage of a concession when there is a need.