Is playing cards (Hand) daily permissible and lawful according to Islamic law, and is specifying certain days of the week for it considered an act of disobedience and disrespect towards one's father, knowing that the father prays at home and does not go to the mosque due to perceived hardship, and that playing relieves the father, even though sitting for hours affects his health?

If your father spends a long time playing cards, then it is part of your dutifulness to him to strive for his reform, to frequently supplicate for him, and to seek assistance from those whom he respects to advise him gently. Remind him that his age necessitates attention to the afterlife, citing the Hadith: "Allah has removed all excuses from a person whose death is delayed until he reaches sixty years." If his condition improves, then praise be to Allah; otherwise, be patient and continue to supplicate for him.

As for preventing your father from playing except on specific days, you do not have the right to compel him to do so, and this might lead to disobedience if he is harmed. The most you can do is persuade and advise him gently, without violence or abuse. It is also advisable to encourage him to pray in congregation at the mosque and to explain the error of his assumption that the reward is equal if he prays at home.