The obliquity of Uranus is a tricky one to explain, the issue with keeping the satellites in the equatorial plane is one of the problems. Another issue is that giant impacts would be expected to randomise the rotation, yet Uranus has ended up with a rotation period similar to Neptune despite its tilt.
As noted by Morbidelli et al. (2012), tilting Uranus from zero obliquity with a single giant impact runs into the problem that while the circumplanetary disc can realign with the planet's equatorial bulge after the impact, the sense of its rotation would be retrograde. This does not match the present-day system, where the satellites are prograde.
Rogoszinski & Hamilton (2020) investigate the possibility that Uranus was tilted via resonances between its spin, orbit and the other giant planets. This is the mechanism that appears to be responsible for Saturn's obliquity, via a resonance with Neptune. The process would likely be gradual enough to bring the satellites along with it as they tend to align with the equatorial bulge, while avoiding the rotation period randomisation of a giant impact. In the case of Uranus they find that with the right initial conditions, Uranus can be tilted to about 70°, requiring a much smaller impact to push it into the current configuration, so you could avoid having to reverse the sense of rotation of the circumplanetary disc. This has the further advantage that there were likely to be more Mars-sized objects than Earth/super-Earth sized impactors, so such collisions are less improbable.
In their follow-up study, they investigate whether the right initial conditions are compatible with the Nice model for the formation of the Solar System. Unfortunately getting to the current situation through the spin-orbit resonance mechanism appears to take too long.
Currently there does not seem to be a particularly satisfactory scenario to explain the rotation of Uranus, but it does appear that the process of tilting the planet was more complex than a single giant impact, and the satellite system is one of the indications that the simple scenario is unlikely to be correct.