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Hmm I'm not really sure if there are other stories like gakuen babysitters but there are two stories i know that you might like, its family-ish
Aka-chan to boku
Its a story about two brothers that has lost their mom, theyre ages are pretty young like one is in elem (not sure) other one is still a baby
And the other one is Love so life
Its gonna be focused on romance in the later chapters but its cute family fluff
http://www.mangago.me/read-manga/love_so_life/
is there any story, involving small kids, the story revolve around them, etc, gakuen babysitter