First of all, it seems a little ridiculous that someone who's been with the company for a while would be on the verge of quitting after only 3 months of working with a newbie. If anything, it is far more likely that this person would come talk to you about it, or already has other grievances that you're unaware of (perhaps working with those other two has driven them up the wall? Who knows.)
Either way, it seems like you have some fact checking to do.
Bring the third team-member in for a private conversation, and ask them what their opinion on the situation is. Be subtle, and let the employee vent. Steer the conversation based on their statements:
Thank you for coming to see me, [Name Here]. I've heard rumors of some tension in the team, and I wanted to ask you whether you feel this is the case.
See what he says. Maybe he'll refute the claim on its face. Or perhaps he'll say that yes, things have been a little strained lately. You can then maneuver the conversation such that you give this person the opportunity to voice any concerns about their newest team-mate. If nothing comes up you can end the conversation like so:
Thank you for bringing these issues to my attention. It's something I'll look into, and please don't hesitate to speak to me about any future concerns. By the way, before you go, how are things working out with the newbie? Are you guys getting along?
See what he says.
Last but not least I'd also bring in the newbie for a 1 on 1. Ask her how she's adjusting to the environment, and how she's getting along with the team. Are there any projects she's struggled with? Why? Which challenges did she enjoy most, and which did she find frustrating?
Allow her to vent, and look for patterns: are the issues she's been frustrated with all a part of projects where she's worked with the two trouble makers? It would be very telling if that were the case.
What I would also suggest is that going forward you would start having at least monthly 1 on 1 meetings with your developers, and allow them to speak to you about anything that may be on their minds, from how projects are progressing, to whether they're excited about the latest Star Wars movie. Get to know them as people, and you'll find these sort of conflicts easier to get to the bottom of in the future.
As far as training for the newbie is concerned, you are her manager, and you need to take decisive action if you feel she needs more mentoring. If the training office is ignoring you, find some sort of online course or webinars that she could attend, and schedule time for her to do so.