child very close to their grandfather
Describes a child who has a strong emotional bond with their grandfather, often preferring his company.
See also: おじいちゃん子
Our daughter is a grandpa's girl and always wants to go to her grandfather's house on weekends.
child doted on by their grandfather
Focuses on the grandfather's affection and indulgence toward the child, rather than the child's own attachment.
He was doted on by his grandfather and grew up spoiled.