Hateship Loveship (2013) on Netflix

Plot summary

Johanna Parry arrives in a new town to take up a post as housekeeper and caretaker. Her employer is Mr. McCauley, an old man who cannot manage his home alone, and she is also there for his granddaughter Sabitha. Ken, Sabitha's father, lives in Chicago rather than in the house. When Johanna asks Edith, Sabitha's closest friend, about Sabitha's mother, Edith says Ken's wife died some years back. After Ken has Johanna and Sabitha over for dinner, he writes Johanna a brief friendly note that Sabitha delivers. Johanna answers it, and Edith volunteers to mail the letter. Edith and Sabitha keep it instead, invent a love letter in Ken's voice, and open an email account in his name to carry on the correspondence. Johanna writes back to every message, sure that Ken is falling for her.