There are 3 different contributions to the magnetic hyperfine field, the spin-dipole contribution B_dip, the orbital contribution B_orb and the Fermi contact contribution B_Fermi.
For the illustration of B_dip I would sit the child into the carousel that is not moving and let it hold the bar magnet in its hands. The magnetic field of this bar magnet can then be measured by the magnetometer that is placed in the center of the carousel. So the field due to the spin of the electrons reach to the position of the nucleus.
For the illustration of B_orb I would ask the child sitting in the carousel to hold the electrically charged ball. Then I would turn the carousel such that the charged ball is orbiting around the magnetometer placed at the center of the carousel. The charged ball creates a ring current that is creating a magnetic field that can be measured by the magnetometer provided that the carousel is turning. So the orbiting electrons create a magnetic field at place of nucleus.
For the illustration of B_Fermi I would need the imagination of the child. I would explain that the charged ball now has to be inside the magnetometer and that there is now not only one but a few more charged balls with colors blue and red. If there are not the same amount of blue and red balls inside the magnetometer we could also measure a magnetic field. The two different colors represent the spin up/spin down state of the electrons and if there is a different number of spin up than spin down electrons in nucleus an additional magnetic field occurs.