Hey! Sorry for the late reply!
When you add に to なAdjective it will work like an adverb (adverbs can modify adjectives, adverbs and verbs).
So when みたいな modifies a noun, it describes similarity in appearance, and when it modifies a verb it describes similarity in a manner of doing something (but ように can also modify adjective to also describe similarity in appearance etc).
In this sentence, you have a noun 日本語 and verb 教える with auxiliary adjective たい to modify.
Japanese (language) in appearance similar to Koichi doesn’t really make sense.
But teaching Japanese (language) in the manner (like) as Koichi does makes one and that is what the speaker wants to express.
Is it clear now?