Is dedicating certain days to congregational prayer at home with an elderly father, out of a desire to show him filial piety, better than consistently performing prayers in the mosque, bearing in mind that the questioner usually prays shortly before sunrise?

The virtue of congregational prayer is immense, and it is obligatory for the one who is able. If your father is unable to go to the mosque due to illness or old age, then he is excused. However, if he is able, you should advise him about the virtue of striving to go to the mosque. If he insists on praying at home, or if he is unable, there is no harm in praying with him at home. Combining pleasing your father with praying at the mosque sometimes is better. And know that praying at the beginning of its prescribed time is among the best of deeds.