"She reads you a newspaper". This is so wrong! The combination of " She reads you . . .". or " . . . . you a newspaper". is very poor. What is ironic is the literal translation and word order of the portuguese "She reads a newspaper for him." as an english sentence is both correct in meaning and far better grammar than the 'stock' answer Duo offers here.
There's nothing wrong with the given sentence. In English we can drop the "to" from the indirect object when it comes before the direct object. The other option is:
She reads a newspaper to you.
I'm not sure why you are using "him" when você means "you". Also, I don't agree that reading it "for you" is a good translation. That could mean what the sentence is getting at or it could mean instead of you.