My wife used a regular bike child seat when our youngest son was <2 and the older two (3/4) were in a bike trailer. All she had was a typical women's hybrid bike and a single kickstand. I think some of this is going to be about weight with my wife weighing enough (don't tell I said that) to overcome the added weight of the child seat riding high on the bike. Up until our daughter was 6ish, I had her on a Yepp Maxi on my longtail and as long as she was ahead of the rear axle, I had no issues even if she was leaning over or moving around. Again I have the weight (I'm just inside the range to be considered a Clydesdale) to overcome her weight moving around. For someone more on the petite side, a lower center of gravity setup would be more ideal. Bikes like the more modern longtails using 20" tires or bakfiets style bikes.