The reason why sometimes they do/don't act weird when pushing has to do with the weird way how the push state and its animations are coded.
With the kids following you, differences in movement speed could show some weird stuff related to sprites like in pushing objects or the swinging.
(At least when they're in the same X axis but the vertical/Y axis is different or something).
Also, yes, I guess you just gave me an idea for how the mud texture could look in Brinkaedea.