We commute with our kids (almost 2 and almost 5). We've been using a Chariot (Cougar?) since the younger one was about 5 months old. We chose the Chariot for the ease in which it converts to a stroller, which is invaluable if you want to take the trailer with a sleeping kid into a store with you or if a non-cyclist (like a babysitter) ever picks the kids up from preschool and walks them home.

If you search for my recent thread on "increasing my visibility" there are some great tips for side visibility for a trailer, which is my personal worry (that is, cars see me at 4 way intersections but don't always act like they see I'm towing a trailer--like other posters, I find that cars approaching from the rear are very respectful). I had wanted a bakfiet for the reason you mention but couldn't stomach the cost--but now I'm glad I have a trailer instead. The trailer is actually much closer to you than you initially think, the turning radius is easy to master, and once you drop off the kids you also ditch all your extra weight for the rest of your commute. At preschool, I lock the trailer with a cable lock through its frame; if we're running errands in a part of town with high theft risk I leave the trailer attached to the bike but lock the frame to my rear wheel (and obviously secure the wheel!). If I'm just running into the grocery store I leave it unlocked.

I'm not so sure a trailer actually is an increased risk. If you're struggling with the issue, you might want to look at the website Free Range Kids, which is dedicated to the premise that we stifle children by always focusing on the most horrific but statistically unlikely outcome. (I don't think this particular situation per se is addressed anywhere on the site, but the site's general outlook might be philosophically helpful.) Furthermore, by using a trailer instead of a car (and we use the trailer rain or shine), I feel I'm demonstrating to my kids self-reliance, an active lifestyle, and the fact that you can find joy in even the most mundane aspects of life like commuting.