"Our child likes to read English books."
在 means the action is continuous. 喜欢 means Like and same as in English this is a verb of emotions, which is intrinsically continuous. For a similar reason that it cannot be in continuous form in English, 在 cannot be used here. Removing this character will make the sentence perfectly correct.
《看》 is to read with eyes. 《读》 is to read with mouth (e.g. read out loud-->读课文(read the texts)), or read with mind (study-->读历史学(study history)). If you 《看一本书》, you are probably reading a book as a recreational thing. If you 《读一本书》, you are reading a book as you absorb knowledge from it. You might take notes. You might memorize something in it.