I personally had a bigger problem with the science... I am a scientist and I worked on chaos and the three body problem, there are many elements in there that just killed my immersion by being wrong. One of them was the mathematician that was computing the solution to the three body problem. No sane person would consider that worthwhile! Chaos means sensitive dependence on initial conditions. Between other things, that means that any error you are making is going to be exponentially magnified in finite time. So if you only considered 3 digits of accuracy in your solution, you can just throw your solution away after a couple of time steps. But if you considered 30 digits of accuracy? well... you only get one or two extra time steps in which you solution still makes a little bit of sense! Check out this youtube video on the double pendulum, another well-known chaotic system, to get a feeling: https://youtu.be/ldnEHycw40E
Still talking about math, when the "the baby problem" planet is kicked away from the two-stars system, likely it would not be able to ever come back. Assuming the planet never actually leaves the solar system is quite a large assumption.