A agree with Cyccommute on the ability of children to do long rides. Just like adults, they need to be trained, to develop their bicycling skills, to toughen their rear end, etc. I have had successively an Addams Trail-a-Bike, a Piccolo trailercycle and now a Co-Motion tandem. No Alleycat, though.
The Trail-a-Bike attaches to the seatpost of the tractor bicycle. The major problem I found with it is that the universal joint developped some play over time. WHile the trailercycle was quite stable at the beginning, it could wobble by 5-10 degrees when I abandoned it one year and 1800 km later.
My Trail-a-Bike was the single-gear model, and I think the gearing was way too high to be useful. I should have changed the cog for one that was 4-6 teeth larger.
By comparison, the Burley Piccolo attaches to a special rack, and the hinge is vertically in line with the rear wheel axis. As a result, wiggling actions by the child don't affect the tractor bike as much. Another strong point is that the articulation uses a ball-bearing system: like a headset and bottom bracket assembly, so it doesn't develop play over time.
One difference between a trailerycle and a tandem is that the child doesn't need to pedal all the time. There may be good and bad points about it, but I think that at a young age, it's a good idea to let the child coast at times. With my eldest, I noticed she learned gradually the skills. The first rides we did on the Piccolo (at 5 y.o.), she didn't shift; then she played with the shifter, then she tried to find an appropriate gear, then she tried to spin more or less in the same gear as I did.
As for the tandem, it's even more stable. Since the kid-stoker doesn't need to touch ground while pedalling, it is possible for a 7-8 year old child to use a small tandem with crank shorteners. When we got the Co-Motion (23"-18" size), MBS Tandems installed a rear seatpost that allowed the saddle to be slightly closer to the seatclamp, and I installed the pedals on 125-mm arms. A few months later, I extended the pedals to a 135-mm circle, similar to what she has on her single.
In terms of stability, the tandem is light-years ahead of the bicycle + Piccolo, which is light-years ahead of the bicycle + Trail-a-Bike. And since my stoker was already used to cycling a lot with me, including pacing herself to my rythm, the learning curve wasn't too bad.
In terms of distance, the longest I could ride with my then 4-year-old child was 80-90 km; her maximum distance per day hasn't increased too much over the years, but she actually cycles all of it. I am sure we could ride more than that in a day, but almost all our rides occur around Montréal, which means lots of red lights, stop signs and the like.
BTW, now that the eldest rides on the tandem, the youngest uses the Piccolo. She is 4 and hasn't found any use for gears yet, so I have blocked it around mid gear.