Light does have inertia, or at least momentum; your setup wouldn’t work. However, if you had a light source that was powerful enough to do what you have in mind, you could just point it backward, and it would work like a thruster.
When beginning the retrun trip, drop a big mirror/sail in space, such that is oriented towards the sun you are moving towards. Now you attach a smaller sail to your ship that is only reflective on the side facing the big sail behind you. Light bounces off the big sail, is focused towards your sail, and propels you. The big sail is also being propelled backwards. That makes the propulsive force steadily weaker, but still positive. You can drop another big sail when needed to get a jump.
(Yes, this assumes a lot of technologies)
Idea courtesy of Robert Forward, Future Magic, 1988, p. 101. Any flaws are probably due to my poor understanding.