I believe Okeke's change of heart at the end of Chinua Achebe's short story "Marriage is a Private Affair" is perfectly plausible. For eight years, he resisted seeing his son and his son's family because Nnaemeka had refused to marry in a traditional way and chose a girl outside his ethnic group to be his bride. Okeke initially cannot accept Nene, but, when she sends a letter informing him about the existence of his two grandsons, and their request to be taken to their grandfather, he seems to soften his stance.
Achebe comments that Okeke begins to lose the resolve he had built up over the years. The storm that blows through his village at the time he is considering the letter is symbolic of his inner turmoil. While never explicitly detailed, the suggestion at the end of the story is that Okeke will give in and see his son and family. Okeke even worries that he will never be able to make up the lost years to Nnaemeka and Nene. The theme of the story is that familial love is the most important thing in life and can overcome cultural and generational conflicts. Thus, it is not surprising that Okeke would alter his opinion after discovering the existence of his two grandsons.