Is it permissible for a woman to pray in the mosque, or is it better for her to pray at home? And what is the way to encourage a father to perform prayers in the mosque?

There is no harm in a woman praying sometimes in the mosque, as the Prophet, peace and blessings be upon him, permitted it by saying: "If the wife of one of you seeks permission to go to the mosque, do not prevent her." However, a woman's prayer in her home is better, and several hadiths indicate this, among them: "Your prayer in your house is better for you than your prayer in your private chamber, and your prayer in your private chamber is better than your prayer in your courtyard, and your prayer in your courtyard is better for you than your prayer in the mosque of your people, and your prayer in the mosque of your people is better for you than your prayer in my mosque." If a woman goes out to the mosque, she must avoid perfume, be covered, avoid crowding men, and ensure there is no fitna (temptation/strife). As for your father, you are only required to remind him of the virtue of congregational prayer for men politely and gently. You can use audio clips or booklets.