“Darth Vader is your grandfather.”
There’s no easy way to tell someone that they’re related to one of the most evil men in history, no pleasant way to share information that will shake them to the core. The best thing to do is be upfront, be honest and be willing to talk about it, but Han and Leia did none of these things with their son, Ben Solo. Leia waited for years hoping that the opportunity to tell Ben of his lineage would present itself, undoubtedly keeping it a secret to protect him from the pain it would cause. Unfortunately there’s no such thing as the right time to tell someone their grandfather slaughtered little children and became a monster.
However, Leia’s efforts to find the perfect moment were taken away when her political opponents publicly exposed her relationship to Darth Vader in an effort to ruin her chances of overseeing the New Republic. While they succeeded in preventing her from taking power, what they could not predict was the side effect the news would have on her son. This revelation was potentially the moment that started Ben down the path to fill the void left by Vader’s death.
To understand why Ben was willing to join Snoke we need to look back at a few factors of his life prior to The Force Awakens, some which have been revealed and others we need to deduce from common human behavior. The first thing to examine is Ben’s relationship with the Force. Pablo Hidalgo states in The Force Awakens Visual Dictionary that there is something about Ben that makes Snoke believe he is “the ideal embodiment of the Force, a focal point of both light and dark side ability”. This is not some sort of prophecy like with Anakin Skywalker, but the natural way Ben is connected to the Force. Snoke was able to feel this power in Ben from a very young age and as a result started to pull him towards the dark side early on.