Is it permissible for a father to prevent his daughter from going to the mosque on Fridays and to prevent her from wearing the hijab out of fear for her safety from problems?

No one is permitted to command that which contravenes the command of Allah and His Messenger, and whoever does so must repent. The hijab (definition) is obligatory by the consensus of Muslims, and a father is not permitted to order his daughter to remove it. She is not permitted to obey him except in the case of fear of certain harm befalling either party. However, mere fear or expectation of harm does not permit the removal of the hijab. As for a father preventing his daughter from going out for Friday prayers, there is no harm in that if he fears temptation for her.