It seems there are really 2 questions here:
私は妹に新しいおもちゃを買いました。
is completely standard. に binds to a noun and marks is as indirect object, i.e. you bought the toy to or for the/your little sister.
In the other sentence, something else is going on:
よい子になるには早寝早起するコトです。
In order to become a good child, you have to get up early and go to sleep early.
The easiest way is to read this as a fixed construction ~には~ used for expressing "In order to something, you have to something / something has to happen". Note that you can't use には to mean "in order to" generally, the "have to" part needs to be there, e.g.
*よい子になるに(は)早寝早起した
He got up early and went to sleep early in order to become a good child
is ungrammatical. It would have to be e.g. よい子になるために早寝早起した
A bit of background is that Japanese used to have zero-nominalization, i.e. you were able to attach case particles to verbs as is they were nouns. In modern Japanese, this is not generally felicitous, but survives in many fixed constructions.