I saw a post on Streetsblog.net talking about a problem a cyclist had with a motorist and his bike and child trailer. He has his daughter in the trailer and got buzzed closely at an intersection. The cyclist blamed the motorist.
I am taking the reverse position in this regards. I do not like to see bike trailers on roads. To me this is just too dangerous and not worth the risks to the child. There are other options, bike trails or roads in housing developments.
A better alternative is to get a good tricycle or small bike for the child. Walk with the child while she rides, more exercise and a better all around activity. I used to jog and my youngest rode his bike next to me. He loved it and we both got exercise.
Or if lucky like me, we had a large hospital parking lot near by, which was most times half empty and especially on weekends. We would bike together to the lot and then play bike games at the lot.
In the Philadelphia area we have many trails for parents to use with children and trailers. I do plead with those parents who think dragging a child in a trailer is safe to find something else to do with the child.
A trip to a park comes to mind. Swings, slides and climbers, way more fun for the child. But get rid of the trailes, just tooooooo dangerous.