I think that depends how fast the thing is going - if it’s a decent fraction of c, there may be no viable trajectory around the target star that would result in a 180 degree turn
One solution is to have 2 of them. As for why you would jettison the first one would be the chance of it entangling the probe, near certainty that it would be torn apart in the interstellar journey, complex mechanism to re-stow it, and increased uncertainty that the restow will work, especially towards top speeds.
Alpha Centuri system has 3 stars, this may give additionally opportunity for additional steller sail braking .
You may not be able to control it directly, but you could re-programm it regularly, updating it as technology advances, so it might be able to do things we cannot imagine now with technology we have installed in that probe. Just as New Horizons was reprogrammed to go to another object (486958 Arrokoth) in the Kuiper Belt after passing Pluto, which was not orignally foreseen. I think the object was not even known when New Horizons was launched.
Too late!: Solar sail - Wikipedia
The nearest known black hole is about 3000 light years away. We don’t have that kind of time available. 
As one would expect from a relatively stable 3-body system, the third body is not very close to the system barycenter. At present, Proxima Centauri is about a fifth of a ly from the AB pair. That is a whole lot of distance to cover after braking there (and Proxima itself has at least one planet or interest).
The separation between the primaries is something on the order of our greater solar system (ranging from the orbits of Saturn to Pluto), so it may not be the ideal candidate for exploring assuming your goal is to find habitable planets. Having a stable solar system like ours seems more than a tad unlikely. But it is almost certainly a very interesting place – the trojan points should be worth giving some attention to.
alpha Cen A and B are too similar in mass to have proper Trojan points. They’d still have Lagrange points, but all of them would be unstable on longish timescales.
I thought L4 and L5 Lagrange points are the Trojan points?
Yes, but their stability depends on one of the two primary objects being significantly more massive than the other.
Assume we send the probe there at 10% lightspeed. We want it to arrive within one human lifetime.
then:
A fly-by will mass 1/100 000th as much as a craft capable of stopping. At least. Possibly a much higher factor, as it could not use an assist from ground-based systems (laser pusher, for example, could be used at launch, but not at stop)
Communications will take 4 years to get to earth, and command will take another 4 years to get there.
It is LUDICROUSLY unlikely that we will be able to communicate out to the spacecraft in any case. If the craft has a 1m dish, and we are using the whole earth as a transmitting antenna, then by laws of physics the craft will receive at most 1 part in 10^26 of the transmitted signal.
Even for us to receive a signal from the craft will be hard, but at least we can cheat a bit by building a ginormous receiver. Possibly even an interferometer array spanning between the earth and moon.
Sorry, but space.is.bigger.than.you.think.
“Space is big. *Really *big. I mean, you may think it’s a long way down to the chemists’, but that’s peanuts compared to space.” - Douglas Adams (paraphrased)
If we can build a ginormous receiver that can receive signals from a small antenna on the probe, we can build a ginormous transmitter that can reach an equally small antenna on the probe.
The ginormous receiver is 237 radio telescopes around the world. Making that into a transmitter is not a simple inverse operation.
Here’s another good article about solar sailing technology, reviewing the state of the art and future challenges:
https://www.sciencedirect.com/science/article/pii/S1270963818314391#!
I think you are describing long-baseline interferometry? Those are used to achieve high spatial resolution. Sparse interferometers aren’t very useful for detecting very faint signals, or transmitting a very powerful beam. Arecibo is a much better communication antenna than VLA.
Once the probe arrives and (hopefully) begins its mission, the round trip communication might take about 8 years. What we can’t forget, however, is the amount of time it would take for the probe to even arrive in the first place. With our technological advances being what they are, it would be completely obsolete long before it ever even arrived. Does it even make sense, then, for us to spend all the time and money to launch one in the first place?
The Voyager probes were launched 42 years ago. The science instruments are “obsolete” in the sense that we can make much better ones now. Yet they haven’t been overtaken by any newer spacecraft, and they became the first spacecraft to make in-situ measurements of interstellar space.
Besides, technological advances don’t happen on their own. They happen because we build stuff and gain experience. If we don’t build and fly interstellar probes, how would we learn to build a better interstellar probe?
The Space Shuttle flew into early this decade using 8086 powered computers. lt became hard to obtain replacement chips for the logic boards, but the computers functioned in 2011 just as the had in 1982. New tech is not necessarily better than the old tech, if the old tech still works.
OK, that is a bit of a drawback.
Having said that, even in the best case, it’s still highly likely that nobody who works on the project will live to see the end result
Because human aging is a harder problem to stop than building a fusion or antimatter powered starship that will have a good chance of working over a centuries long voyage?
Get real.