I wish to read English with my children. They are preschool age and have no English. I began by substituting the bedtime story with an English story but they got frustrated by the fact that they didn’t understand and suddenly they disliked the bedtime story. So I remedied the situation by reading one sentence in English before I translated this sentence to our language. I then read through the book this way. I notice they are learning to recognize English words, as they point them out when they hear them. I’m just trying to expose them to English anyway. Is my approach a good one or have you an alternative approach?
The natural way of language acquisition is based on associating words with situations.
So I'd recommend to present a story not only in oral English, but also with some other means, like pictures, gestures and so on, so your children have something they can associate the foreign-sounding words with. But I doubt that such a more action-based approach fits well with the purpose of a bedtime story, i.e. preparing the children for a restful night.
The problem I see with your second, two-languages approach is that the children will associate English words with native-tongue words, and that's not useful for getting fluent in a foreign language, as it forces their mind to actually handle two languages at the same time, while in a real-world English-language situations the native language is only a hindrance.
[To me personally, I find it much easier to communicate in English than to translate between English and my native tongue, German. Quite often I find that an English word that I perfectly understand and use, doesn't have a simple German equivalent, so I have to think hard to find a proper translation.]
Instead, I'd try to use English from time to time in everyday life, in situations that your children clearly understand, so they can associate the language with well-mastered concepts.
I don't know your opinion on TV / movies etc. for your children, but to me as an adult learner, watching TV shows has helped me a lot. So maybe watching something appropriate for your childrens' age in English might be another idea.