El Pequeño Lord (1988)

The story concerns an American boy named Cedric Errol (more fondly known as Cedie[1]), who at an early age finds that he is the sole heir to a British earldom and leaves New York to take up residence in his ancestral castle. After some initial resistance, he is joined by his middle-class mother, widow of heir James Errol. His grandfather, the Earl of Dorincourt, intends to teach the boy to become an aristocrat, but Cedie inadvertently teaches his grandfather compassion and social justice, and the artless simplicity and motherly love of dearest warms the old man’s heart.

Source: www.anisearch.com/anime/613