Why "I gave my brother a book" but "I gave a book TO my brother?"
A language companion asked me "which is correct?" I said they were both perfectly correct and natural, and mean the same thing except for a subtle difference in emphasis. Then she asked me "why do you need the word 'to' in the second sentence, but not the first?" I was stumped. In both cases, "book" is the direct object and "my brother" is the indirect object, but we need "to" in one of them and not the other. And the other way around is actually wrong; "I gave to my brother a book" is wrong, "I gave a book my brother" is... comical (it means I offered my brother as a gift, to a book!)

Question

Why "I gave my brother a book" but "I gave a book TO my brother?"
A language companion asked me "which is correct?" I said they were both perfectly correct and natural, and mean the same thing except for a subtle difference in emphasis. Then she asked me "why do you need the word 'to' in the second sentence, but not the first?" I was stumped. In both cases, "book" is the direct object and "my brother" is the indirect object, but we need "to" in  one of them and not the other. And the other way around is actually wrong; "I gave to my brother a book" is wrong, "I gave a book my brother" is... comical (it means I offered my brother as a gift, to a book!)

Answer

Hi Dan! :)

Well, the way I explain it is this: if a verb has an indirect and a direct object, the indirect object can sit between the verb and direct object without a preposition. In any other position, you need a preposition for the indirect object.

Where most students stumble is that they're not often aware of which verbs naturally take both indirect and direct objects, and they end up following their first-language grammar.

May I ask where the language partner is from? This might explain some confusion, if she's replacing English grammar with grammar from another language.

Answer

Hi, Dan. The rule of thumb is that native-speakers generally put the indirect personal pronoun between the verb and the direct object. (I gave my brother the book. He lent me some money. She got him a cup of coffee.)
BUT
When the object is long, we put it at the end. (I gave the book toTHE MAN IN THE RED HAT SITTING AT THE END OF THE BAR).  (She lent the money to HER UNCLE ON HER MOTHER'S SIDE). (I got a cup of coffee for THE HOMELESS MAN SITTING IN THE RAIN).  We should all buy him a cup of coffee, by the way.

Answer

I think the key is, as you said, the subtle difference in emphasis
Consider what the question would be for each statement
What did you give your brother?
"I gave my brother a book" - emphasis on book, which is the direct object
Who did you give a book? or Who did you give a book to? or more traditional style, To whom did you give a book? 
---key point--- to whom
"I gave a book TO my brother"