I think it is perhaps unwarranted to say people apprehend their sense of reality as Dasein. The first reason for this is that 99.9% of people are unaware of the existence of the word, let alone the complex concept which Martin H. designed for its use. The second reason is that the notion, where understood is contested. Contested as an idiosyncratic theory of existentialism. But thirdly, I think Martin H. was of the opinion that only a few select people would ever be capable of coming to terms with their existential reality.
Most of us accept a disunited reflective and objectivised reality and so are in denial of the true Dasein self.
I always used to think that a two year old is more close to true Dasein than older humans. But there is an element of Mr. H. requiring the child to come through the objectivising and reflectivity to return as an adult to the true inner self. And only a few achieve this.
Maybe the self interested child is the best place to begin to understand Dasein. Did Martin H. ever say anything about other mammals?
I think the reason you might be stuck is applying “values” to Dasein. You can’t have a value without comparison. Values can’t exist wihout evalualtion. You cannot make a comparison without reflection, and you loose sight of Dasein when you reflect. Dasein has to remain the root of being, having no value but its own. And I don’t mean “values”. Dasein is all self-(value).