Interesting, getting their hair stuck in your teeth reminded me of the phrase "get in someone's hair, Slang. to annoy or bother someone."
You seem to find it a bother (and perhaps unnecessary) to have to go "through" all those people. Oh - and, "go through" "2. To be initially screened or handled by another person." Perhaps you felt quite "motherly" at the time of the dream despite not having a child at the time? You were annoyed that you had to handle so many "strangers," to perhaps "check them" first before your daughter went through them, you were trying to protect your daughter. But you were getting annoyed because you felt like you were annoying people in the process. Your daughter does not seem to realize how you are feeling about this until you tell her, and then she agrees to make it a little less unpleasant for you.
