I love how in your Obi-Wan's lie timetravel AU universe Anakin has a reasonable suspicion that Ahsoka could be Vader, the end of all Jedi, Padme's killer, EVIL and his response is "extra meditation, that should help." It's like, wow Anakin, you get attached really quickly huh? Luke clearly takes after him - you know if Obi-Wan fell or Snips or something Anakin would be *certain* they could come back to the light and also would still love them despite everything
To be fair to Anakin in this AU, his initial plan for her wasn’t just “extra meditation”. But that’s only because he didn’t actually think far enough ahead to have a plan. He panicked and claimed her as his own to keep her away from Obi-Wan and to keep that potential future from coming true, then panicked when he realized he had no idea what to do with a padawan??? Let alone a padawan who could spell Doom for everyone he loved. And it wasn’t like he could consult anyone on the matter, as Luke had sworn him to secrecy.
So Anakin alternated between determinedly Not Thinking about the entire thing and trying to impress certain morals on Ahsoka in order to prevent her from becoming Vader. As you can imagine, this often didn’t go particularly well…(Anakin: “Killing is bad, Snips. As Jedi, we don’t do that.” Ahsoka: *blinks in confusion* “I thought we were fighting in a war? And weren’t you just bragging about the number of B1′s you downed?” Anakin: “OK, but that’s different. You can kill droids and Separatists! Just… nobody else. Morals!!1!!!”)
The extra meditation was a combination of happy coincidence (he could keep an eye on both Obi-Wan and Ahsoka at the same time this way!!) and intentionality (he might have obliquely mentioned to Obi-Wan that he was concerned about his apprentice and Obi-Wan might have suggested additional meditation – Anakin refused to give any specific details about his concerns, after all, and this kind of limited the suggestions that Obi-Wan could make).
Oh yeah, Anakin definitely wouldn’t have given up on Obi-Wan or Ahsoka had they Fallen. Though, depending on the circumstances, he might have followed them into the Dark instead. (That said, if Palpatine had manipulated things properly and made it seem as though Obi-Wan or Ahsoka had somehow personally betrayed Anakin in addition to going Dark… well, that might have changed things.)