Wandering Sun

 Two baby girls were born in the same hospital: one of them is the daughter of an aristocratic family while the other belongs to a depraved household which lives in the slums of the city. However, the nurse-in-charge, Michiko, secretly switches the two babies due to a personal grudge, resulting in a change of fates of the girls from then on. Many years later, the lives of the two girls continue to be intertwined with each other, with the rich Miki ill-treating the poor Nozomi, yet both of them hold similar dreams to become a singer.

(Source: Anime News Network)