You are on the street level, so you know best what your roads are like, but your mention of your current trailer being "too wide" for your route gives me the impression that you are hugging a shoulder and trying to stay out of the way of the traffic. Though it seems counterintuitive, the fact is, you are far safer as a cyclist if you TAKE UP MORE SPACE in the road, OUT OF THE DOOR ZONE AND OUT OF THE SHOULDER. In other words, you ARE traffic, don't be afraid to act like it. While you are hugging the shoulder, dar drivers that can't see you or think they can squeeze by without slowing down will whip by you, creating far more hazard and likelihood of harm to you, than if you occupied your rightful place a foot or two to the left of the white edge line, and let the traffic see you, slow down and go around you. All of this is especially crucial when you are traveling with a child. (It's nerve wracking, but I did it myself for years, when my own kids were small.) Using a double wide kid trailer might give you an even more imposing profile, and also make you more safe.
And congrats on your accomplishment -- it's a big deal to step outside your comfort zone and try the new thing.