This may be a somewhat self-selected group in which to ask the question, but I'm interested in what road conditions (speed, shoulder, traffic level etc) people accept when towing small children.
I live in a suburban area criss-crossed with train tracks, rivers and an interstate. For recreational riding with kids there are wonderful trail options. However, transport (I'm trying to get car-lite-r) is more problematic. On quiet neighborhood streets I am very comfortable, and I tend to ride lit up like the proverbial Christmas tree (in daylight). Going any appreciable distance involves crossing tracks / river / interstate, and only the 40mph arterials (with 50mph real speeds) actually do this. Towing a trailer through a high-curbed, unlit, pot-holed underpass with 50mph traffic is not my idea of a good time.
The alternative is to take to the sidewalk for .5 - 1 mile stretches. This obviously requires going very slowly (to properly monitor turning traffic) and I walk any major crossings. Drivers around here aren't even expecting pedestrians in these spots, for the most part.
Alone (or towing inanimate objects) I do ride in traffic when necessary; I try to select quieter routes as a risk management strategy, but I'm basically comfortable. And I'm assuming my own risks. It may not be entirely rational but I find it very hard not to feel differently with a child on board. Honestly, I'm inclined just to drive this sort of trip.