The ice giants are migrating very little, and any migration that they undergo is certainly not for the same reason that Earth’s Moon is moving away from us. Many factors affect orbits of large bodies, which are actively fluctuating, if slightly. But two key factors are tidal interactions and the distance between the two bodies.
Earth’s gravity keeps the Moon in orbit around us and the Moon in turn causes the oceans’ tides. The side of Earth that faces the Moon feels a bit more gravity, while the side facing away feels less, creating a slightly oblong Earth. Called tidal bulges, these oblong areas can occur on solid ground, but are most noticeable in the ocean. Earth’s rotation means that the tidal bulge facing the Moon will always be just ahead of the Moon, pulling our natural satellite forward. This gives the Moon a gravitational boost, pushing it farther away.
But the Moon is only 60 Earth radii from us, whereas Uranus is 4,000 or so solar radii from the Sun. So, the tidal influence of the Sun on Uranus’ orbit is smaller by around 16 orders of magnitude (that’s a factor of 1016). The effect for Earth or even Mercury is much larger but still negligible. It is likely, however, that Mercury’s and Venus’ spins experienced some tidal influence, slowing their rotation somewhat since they were first formed.