There are no planets in our solar system that "trade orbits". Orbits are determined by gravity and are relatively stable over very long periods.

It's possible you're thinking of orbital resonance. This is where two celestial bodies have a gravitational relationship where their orbital periods are related by a ratio of small integers.

For example, Pluto and Neptune are in a 3:2 resonance. For every two orbits of Neptune around the Sun, Pluto completes three. This isn't them "trading orbits", but rather a complex gravitational dance.