Call it the other sixth sense if you will - proprioception is the body's sense of its parts and limbs in relationship to one another. What allows us to drive without staring at our feet to make sure they are moving the way we want them to. Like the vestibular sense, this is one of the eldest and most basic, evolutionarily speaking. Which is why stimulating it, just like stimulating the vestibular system, is so reassuring and calming for kids.
Hugs are a classic form of joint compression and muscular pressure. As is massage! Yogis from my Baby and Tot classes will recognize Heartwarm Touch and my instruction to use firm (but still gentle, obviously) pressure when doing infant massage with their little ones. This is because a firm touch reinforces a developing child's sense of their body's boundaries - lighter touch tends to be more stimulating (for an adult translation - think of the difference between being tickled by a feather versus being kneaded by a deep tissue massage!).
Tykes class yogis will reconize burrito rolls (using a yoga mat, parents and preschoolers take turns rolling each other up and then "eating" their burritos) as a fun opportunity to provide gentle joint compression and muscular pressure. And doing blanket swing, in which a child lies down length wise in a sturdy blanket while two adults gently swing her back and forth while singing, provides both joint compression AND vestibular stimulation!
Babywearing and infant swaddling also stimulates the proprioceptive system. For preschoolers, try a "human swaddle" - spooning and hugging your child in a dark room at night can be extremely soothing.