They are just 4 years old, so they are not able to read Korean characters.

Can replace "just" with "only"

But they really like to read books whenlisten to me and my wife or I reading aloud.

In the library, they were amazinged by a lotthe number of books.

One of the kids said there were more books than in our home.

They selected three books to borrow, and brought them home.

I read them aloud, and they enjoyed listening to ithe books.

We made an appointment that we will goo return to the library again.

But they really like to read books when my wife or I read them aloud.

You have used the word "read" twice (correctly), but they have different meanings.
Your children read books = they look at the pictures
You/your wife read books = you read the words
I've just added the extra word "them" to make the sentence more clear. Otherwise, it sounds like you're saying your children read the words (which they don't, yet).

In the library, they were amazinged by a lot of books.

We use "amazed" to describe an emotion that a person feels.
We use "amazing" to describe the thing or situation which causes to feel an emotion.

E.g. "The library was amazing. My children were amazed (by the books)."

We made an appointment that we willo go to the library again.

You can use the set phrase "to make an appointment to... (do something)".
E.g. "I've made an appointment to see the doctor."