Would the prayer of a father be accepted if he does not complete his ablution, does not shield himself from urine, and prays under duress out of fear of his son, with the son believing that he will stop praying once he returns to his country?

We ask Allah to reward you for your dutifulness to your parents. You should supplicate for your father's guidance. As for the ruling on his actions: not concealing oneself while urinating, when capable, is forbidden, but it does not affect the validity of the prayer. What does affect it is not performing istibra' (ensuring no urine drops remain after urination), which is a major sin, and prayer is not valid without istinja' (washing after relieving oneself). You can help him with cleaning and wudu'. If he sees you assisting him, he might strive to perform wudu' correctly.

As for his negligence in wudu' by not completely washing his face and arms, wudu' is not valid with this, nor is the prayer. He must repeat the prayers he performed with this wudu'. So, repeatedly advise him gently, remind him of Allah and His blessings, and seek help from someone who might influence him.

It is permissible for the sick person to combine prayers, either by bringing the later prayer forward (taqdim) or delaying the earlier prayer (ta'khir), if needed. Perhaps if he combined the two prayers, it would be easier for him, and his desire to pray would increase.

As for him praying out of shyness from you: he might intend to pray without your knowing. But if he prays only out of shyness from you, this is pure riya' (showing off), and he has no prayer, and his deed is worthless.