Leia ended her Jedi training, seen in Ben Solo crossed over to the dark side, becoming Kylo Ren. He left his family behind, choosing to serve Snoke and the First Order, even leading his own group of followers and Force-s, the Knights of Ren.
In The Rise of Skywalker, a The Last Jedi). However, she has a vision of her son turning evil if she continues down the path of becoming a Jedi, and so puts an end to her training. Instead, she eventually sent her son to train with Luke, but it wasn't enough to stop him from being consumed by the dark forces at play inside his head.
There is, however, a sense of a self-fulfilling prophecy at play here. By choosing to act, rather than letting things play out, Leia unwittingly sent Ben Solo on the path that would lead to him becoming Kylo Ren. It begs the question: if Leia had trained to become a Jedi, would Ben have turned all the same? Since she envisioned it, it is entirely possible that's how things would've played out regardless of her choice. There were certainly other factors involved, not least the manipulation of Palpatine. The novel Aftermath: Empire's End hints that Palpatine was interested in Leia and Han's son before he was even born, and the comic series The Rise of Kylo Ren makes his interest throughout Ben's childhood and teenage years all the clearer. With that, it's easy to believe poor Ben Solo never stood a chance.
At the same time, however, it's still possible that Leia becoming a Jedi might have changed things. Ultimately, a mother knows her son better than an uncle, and so when Palpatine decided to make his presence felt more keenly, which is likely what resulted in Luke sensing the darkness within his nephew, Leia would have reacted differently. Leia, as both a Jedi and Ben's mother, wouldn't have raised a lightsaber to him, not even for a moment, and so the moment that pushed a terrified Ben Solo away and ultimately brought about Kylo Ren wouldn't have happened. It's easy to fall down a rabbit hole of possibilities - the Jedi Temple doesn't get destroyed, Luke doesn't go into exile etc - but a key takeaway is that Ben wouldn't have turned because of that specifically.
Ben Solo had an uneasy relationship with his parents, but if his mother, a Jedi, also trained him in the Force, then it could have been something to bring them closer together. When she pleads with Han to rescue their son in Leia and Ben Solo when they both died, and that could've been shown earlier.
Of course, things might have played out exactly as Leia saw. Palpatine still would've tried to take him, and may have succeeded eventually at one point or another. And yet, Palpatine's strengths work best when preying on the weaknesses of others - it's no coincidence that both Anakin and Ben fell to him, and both had suffered (in different ways) in of their families. With Leia as a Jedi, maybe it would have been enough for a different outcome for Ben Solo than his turn to the dark side and eventual death in The Rise of Skywalker.
