Does not telling one's father the truth about performing Salah, out of fear of embarrassment, affect the acceptance of Salah, knowing that the son performs Salah willingly for the sake of Allah Almighty?

As long as the motivation for performing the prayer is the desire for the countenance of Allah the Almighty, then the prayer is accepted, and the feeling of fear from the father does not affect it. That feeling is nothing but a whisper from Satan to cut one off from the remembrance of Allah and prayer, and it may lead to lying and other sins. The Muslim must be firm, patient, and constant in remembrance and prayer, for that repels the cunning of Satan. Whenever a servant turns to Allah, whispers come to him, so he must turn away from them and turn to his prayer and strive to perform it in congregation; for this is one of the ways to get rid of whispers. Congregational prayer is obligatory according to the more authoritative opinion, and Fajr prayer with the mosque congregation holds a great reward. As for lying, it is not permissible.