Tsubomi-chan, Wasuremono Nai?

Tsubomi falls asleep whenever she tries to be "proper". One day, she falls asleep in the park and wakes up to find herself in the hands of a stranger, Grandpa! She is then taken by Grandpa to the Ariake's, a group of people who are not "proper" - her male mother, her female father and her neglected older brother, Yuki-chan - and becomes the "little sister" of a strange pseudo-family!

(Source: Renta!, translated)