When my daughter was around three, we started out with the trailer bike and then graduated to a tandem with the pedals adapted.
She had been on training wheels on her own little bike since she was two and was doing just fine; being on the trailer bike gave her an opportunity to go places, to feel like a big kid and to develop an appreciation for what cycling can offer. For me, I saw it as an opportunity to be exposed to cycling but even better, it was lots of fun for us both. Sometimes she would pedal, other times not so much. It didn't really matter.
In short order, she was riding her own bike but we continued to use the trailer bike until she was eight when we graduated to the tandem. She would pedal along, talking the whole way, and of course, on the hills, I was on my own. Again, the bottom line was that we had tons of fun and traveled many miles in that way.
Now at 27, she lives in the Boston area. She sold her car and uses her bike as her primary mode of transportation. I seriously doubt that she would have even considered selling her car if she hadn't had that kind of exposure and had developed such positive feelings about cycling.
So, the moral of the story is that perhaps you could see the trailer bike primarily as a way of showing your kid the possibilities as opposed to a way to learn. Much less anxiety for both of you!