Two possible optoins.
1 If the childminder cycles then get a spare Adams trailer-Bike hitch for the second bike. Leave trailerbike at school. Childminder tows child home.
2 Trail-gator. These look pretty ugly but can be used to attach a regular kiddy bike to an adult bike. This way mum tows kiddy to school, drops kiddy and bike. Folds up Trailgator arm and continues to work. Then childminder collects kiddy and bike which kiddy can ride home.
However, I've never heard a good word said about Trail-gators.
Here goes then ...
I've used a trailgator with my elder daughter for a couple of years now, and find it very good.
You do need to spend some time on the initial setup, particularly with respect to adding some or all of the supplied shims so that the towed bike isn't hitched up at too much of an angle, and making sure everything is tight enough, but I don't find much play at all in the hitch. Certainly not compared to some trailer bikes I've seen out and about.
The main advantage over the alternatives is the ability to unhitch at the far end and allow my daughter to ride solo where it's safe to do so.
The main downside is that I need to remove the rack from my bike when towing her, so my luggage capacity is limited to a handlebar bag. If loaded, this tends to exascerbate the feeling of steering wobbliness that the seat post hitch tends to give you anyway (aka "tail wagging the dog syndrome"), but it's easy to adjust to.
I do have one slight concern about the bolt that secures the short square box section (onto which the trailgaotr then attaches via a quick release) to the bracket on the seat post of the towing bike - it's a single steel nylock nut, and appears to have a tendency to loosen over time. I'd feel safer if the bolt had sufficient space to add a second nut as a locknut/backstop , or if it was longer and e.g. drilled for a pin, to prevent the nut dropping off. If I remember next time I'm at the local hardware emporium, I will try and source a longer bolt for that part.
Cheers,
Mark