Yes part of the problem with the childrens' roundabout explanation - which is correct of course as far as it goes - is that the earth's surface is not the plane of rotation (whereas the childrens' roundabout is the plane of rotation). The coriolis force appears in the plane of rotation - so the resultant force parallel to the earth's surface will be different at different lattitrudes. I suppose it is analogous to the variation in magnetic dip at different lattitudes - well sort of. Anyway visualising it is a 3D problem, not a 2D one.
H