Is Jupiter really shepherding the main belt, and Neptune the Kuiper belt? By &quot;dominating another object's orbit&quot; my understanding is that the most massive body's gravity has so much influence that, when they come close, it makes the other body/bodies' orbits shift or change, either certain parameters (such as apoapsis, periapsis, inclination etc.) or up to pulling it completely out of its current orbit (thereby perhaps ejecting the body from it or making the body collide with the dominating body or a satellite of the dominating body). However, as far as I can determine, Jupiter is unable to alter the orbit of Ceres; both of them are in stable orbits, nor can any other of the main belt's equilibrium-shaped object's orbits (Interamnia, Hygiea, Pallas and Vesta) ever influence themselves to the point that one's orbital parameters are altered nor does Jupiter exert enough gravitational influence on any equilibrium-shaped main belt object to alter its orbit.
The same seems to be true for the Kuiper belt: For every two complete orbits made by Pluto, Neptune makes exactly three orbits. So both object's orbits are stable and Neptune doesn't influence Pluto's orbit in a way that it would be altered, nor is any other spherical TNO's orbit manipulated either by Neptune or by themselves between each other.
Am I right and is there even any equilibrium-shaped object directly orbiting the Sun that ever altered another equilibrium-shaped object's orbit in recorded history, or would be able to do so in a close approach? As I see it, all ellipsoidal objects orbiting the Sun in our system are on stable orbits that won't change unless some interstellar 'visitor' might meddle any up.
Orbits aren't knife-point balances of speed, distance and direction. For two objects separated by distances much larger than their diameters, almost any combination of the three where the speed is below the local escape velocity results in a stable elliptical orbit whose specific parameters are determined by the combination.
Ceres (and all the other objects in the solar system) are affected in their orbits by the gravitational influence of Jupiter (and everything else, for that matter). However, because the orbital periods of Jupiter and Ceres aren't low-denomination multiples of each other, the influence of Jupiter, while present, remains small, and the orbit remains pretty much the same, year to year.
Where the periods are a low-denomination multiple of each other, however,  the gravitational interactions reinforce repeatedly over billions of years, and can serve to both alter orbits such that the resonance is no longer maintained (see the Kirkwood gaps in the asteroid Belt), or in specific situations, lock an object into maintaining that resonance.
With Pluto and the Plutinos, the fact that their periods are clustered around 3/2 Neptune's orbital period is a direct result of Neptune's gravitational influence over time, rather than in spite of it; The regularity in the amount and the direction of Neptune's perturbations to their solar orbits keeps them near the 3:2 resonance, similar to the way Jupiter keeps the Jovian Trojans near the 1:1 resonance and the Hildas near the 2:3 resonance.
Note that all the orbital parameters of all the bodies in the solar system are changing over time (For example, the perihelion of Jupiter precesses approximately 6.55 arcseconds per year). The Keplerian Orbital Elements of the planets that you may find online are based on measurements taken at a specific time, and define orbits that assume that the planet and the Sun are the only bodies in the universe.