Rose Wilder was the daughter of Laura and Almanzo Wilder. Rose was the niece of Royal Wilder, Eliza Jane Wilder, Perley Day Wilder, Mary Ingalls Kendell, Carrie Ingalls, and Grace Ingalls. She was the adoptive niece of Albert Quinn Ingalls, James Cooper Ingalls, and Cassandra Cooper Ingalls. She is the granddaughter of Charles Ingalls, Caroline Ingalls, and Almanzo's parents. Rose had a younger brother who was un-named and died a week after birth. She is also the cousin of Adam Kendell Jr. (dead) and Jenny Wilder.
Laura and Almanzo found out that they would be having a baby in I Do, Again. Rose Wilder was born in Days of Sunshine, Days of Shadow. (Part 2 here.) At the time, Almanzo was bitter and angry, the first thing Rose heard her father say was, "Good thing it isn't a boy, can't play ball with your son when you're a cripple." (Episode 817: Days of Sunshine, Days of Shadow (Part 1), (Episode 818: Days of Sunshine, Days of Shadow (Part 2) After a short bit, Rose became her father's little girl gaining the nickname Rosie Posie. Her mother, Laura, loved her more than anything, going to great lengths to protect her. Rose liked to be held and would sometimes cry just for that reason.
Outside of her parents, Rose was loved by her grandparent Charles and Caroline who have no other living grandchildren. Uncles and aunts, both on her parent's side and cousins comment on not being able to wait for Laura to finally have her baby. Jenny watches Rose a lot when Laura and Almanzo are busy. Shortly after the death of brother, baby Rose became very ill and had to be taken to Doc Baker over Laura's objection as she blame him for the death of her son. She eventually got better. (Episode 918: A Child With No Name)
Rose was kidnapped in Bless All the Dear Children, by a woman whose baby has just died. Laura and Almanzo both search everywhere for their daughter and with the help of Mr. Edwards and an orphan boy, find her. (Bless All the Dear Children) She was still a toddler/infant when the TV show ended. In the after movies, it is guessed she ranged from one to four years old.
Laura was inspired to name here child "Rose" when she recalled Cassandra bringing her a Rose the day before she and Almanzo were talking in bed before she was born, and before Almanzo was injured. (Episode 818: Days of Sunshine, Days of Shadow (Part 2)