① He asks me to read the picture book which you gave him every day.
② Every day, he asks me to read the picture book which you gave him.
こんにちは^^
「彼は毎日あなたがくれた絵本をよんでほしいと頼んでくる。」ですね？
① He asks me to read the picture book which you gave him every day.
「あなたがくれた絵本」は、which を使って、the picture book which you gave him と表現すれば言いやすいですね。
毎日を前に出して、
② Every day, he asks me to read the picture book which you gave him.
毎日頼んでくるということを強調してもいいと思いますよ^^
アダム先生＆ミチコ先生
He gets me to read the book you gave him with all the nice pictures every day.
この場合、次のような言い方ができますよ。
ーHe gets me to read the book you gave him with all the nice pictures every day.
「彼は毎日あなたが彼にあげた絵本を私に読ませる」
to get someone to ... で「人に…させる」
絵本は a book with pictures とも言えます。
ご参考まで！
アメリカ合衆国 
ドイツ 
カナダ 
