We can definitively answer as to why Yoda didn't train them, from ROTS novelization by Matthew Stover - "because Yoda said so".
As Yoda, Organa and Kenobi are deciding what to do at the end, Yoda says about training both twins in the future:
"... Hidden, safe, the children must be kept. Foundation of the new Jedi Order, they will be."
"We should split them up," Obi-Wan said. "Even if the Sith find one, the other may survive. I can take the boy, Master Yoda, and you take the girl. We can hide them away, keep them safe— train them as Anakin should have been trained—"
"No." The ancient Master lowered his head again, closing his eyes, resting his chin on his hands that were folded over the head of his stick.
Obi-Wan looked uncertain. "But how are they to learn the self discipline a Jedi needs? How are they to master skills of the Force?"
"Jedi training, the sole source of self-discipline is not. When right is the time for skills to be taught, to us the living Force will bring them. Until then, wait we will, and watch, and learn."
Now, admittedly, as with many wise pronouncements from Yoda, he doesn't explain in detail WHY he made that decision (e.g. he says it's OK that he won't be training them... but not why it wouldn't be OK for him to do so).
In the absence of better detail, I'm going to speculate that he meditated on the Force and arrived at such a conclusion this way as opposed to having deep rational reasons.