Re: "The detached sail will accelerate but the probe will decelerate"
"Why ? This is space, there is no aether to decelerate the probe. The probe will continue at its speed, and the sail, being pushed by the laser, will accelerate further and go faster than the probe.
But the probe has no reason to slow down simply because it detached from its sail."
That was also my first take. Then on careful re-reading : "parts of the sail is detached, reflecting the laser light from Earth to the remaining sail attached to the probe," the idea is to detach one of the sails and keep aiming the laser at it and not at the sail attached to the probe. So probe would go on at same velocity, detached sail would accelerate past the probe. Then when detached sail is far enough in front of the probe, reflect laser from the detached sail towards the forward surface of the sail still attached to the probe, which will decelerate the probe.
And my take on that was: "Holy crap, no effing way!". The theory is nice, but hitting a probe's sails (few hundred m at most?) millions of km away with a laser is hard enough. Hitting one specific sail but not the probe on the main beam AND hitting the probe's sail with the reflected beam is so far beyond our engineering capabilities as to be truly science fiction.
Biting the hand that feeds IT
