correct example: 「うちの子には子供らしく元気に育ってほしい。」
why is it not correct? 「うちの子には子供みたいに元気に育ってほしい。」
can't really understand why it can't be used in this sentence
The reason is that:
「こどもらしい」 has a positive meaning of "child-like" and
「こどもみたい」 has a negative meaning of "childish".
Thus, your second sentence:
「うちの子{こ}には子供{こども}みたいに元気{げんき}に育{そだ}ってほしい。」
practically makes no sense as it means:
"I want my kid to grow up healthily in a childish way."
Your first sentnece:
「うちの子には子供らしく元気に育ってほしい。」
makes perfect sense as it means:
"I want my kid to grow up healthily like a good kid (should)."