If a planet is tidally locked to its star does that reduce the likelihood that its moons would be habitable?
Good question. I'm guessing the dynamic forces would play havoc with the orbit, but it's only a guess.
But even if it survives in the short term, it won't in the long term.
As a planet loses its rotation rate in becoming tidally-locked, the orbiting moon would eventually be orbiting faster than the rotation rate of the planet. This will cause the tidal stress to drag the moon into the planet.
The Moon, for instance, is moving outward because of the faster rotation rate of Earth. [John Darwin (son of Charles) seems to have been the first to discover this.]