It sounds like the ex is capable of insight and also respectful towards you. Counseling training does have its uses in real life when w'r able to slow down our own reactions so we can recalibrate our approaches before they color our outward behavior--which is far easier to do when you don't have your own cerebellar-structured interaction-pattern with the other person--and YOU don't, so you're in a better position to mediate frictions between her & him than she is.
Now that raises the question of how to get your wife to recognize that you are more successful than she in interaction for conflict reduction. You could approach it with the concept of "Good Cop, Bad Cop" because YOU got a partial confession of culpability out of him, that he does let his frustrations out to his son, which he could not easily do with HER. And you didn't tell her (much) about that, I'd guess. So he can be more vulnerable with you than with her. He's also not re-partnered, so he's feeling one-down to her and may also be constellating his own oedipal triangle from childhood with you as the (new) Father. SO any kindness and understanding you show towards him may be both humiliating and (if it does not seem to have a shred of condescension in it--and you can monitor that by watching your own feelings) liberating him from the inner (denied) prison of "I wasn't good enough for her, and she won't let me loose." [That's the paradoxical opposite face of the controlling husband, who is controlling&imprisoning his wife's soul because that's his desperate strategy to make sure she has to love him: That's HIS own Mother-complex &/or Father-complex re-embodied in his LPC.] But YOU can give him a pathway to redemption of his (already in childhood) deformed self-love, by giving him subtle hints on how to improve relations in the whole family and thus earn his own rehab from the guilt&helpless-regret prison--eg by teaching his son about how to show his mother respect even when he doesn't want to trust her, and by gaining his own insight about how the marriage deteriorated and crashed that does NOT rely on the lie that she was cheating.
At some point you might even mention that the BEST thing that a man can do after he's been shoved out by a divorce is to get a year of counseling for his own personal development, so that the next time he gets involved with a woman he's far more in command of his own emotion-colored behavior, AND even his exwife might recognize that he's REALLTY turned a good corner in his behavior and the kids will then benefit from the personal insight he's passing on to them. [otherwise it's possible his boy will grow up to feel 2nd-class like his father and also try to control a girlfriend and get even worse if it works, and it often does, even for the first 3-10 years. (Your kindness towards the boy will help reduce that--same as for the father).
[I mention the idea that his exwife might be impressed with a self-insight-based turnaround in his behavior, because THAT’S WHAT HE SECRETLY WANTS, and needs to GET HIMSELF OUT OF HIS LONELY PRISON of personal FAILURE —where he probably grew up too.]
A further point: They wouldn't be spewing anger & "righteous outrage" at each other if either of them had worked through the anger (from tumultuous emotional chaos) stage of their grief. That would be likely to happen whenever expartners have little consciousness about grief and more motivation to avoid it than to suffer with it, and especially if she got involved sooner than he did, SO HE ACTUALLY FEELS LIKE SHE'S CHEATING ON HIM, because he hasn't even started to let go of her and let her be happy even when he's not happy. (That could be where his accusations that she was cheating come from.)
There is one simple step that both could take to help begin the purging of those undigested emotions: Write a long letter to the other to express EVERYTHING that's waiting inside to come out, LOUD & CLEAR, and explicitly give permission to express ANGER, HATE, HURT, UNFAIRNESS, SORROW, DISGUST, SHAME/HUMILIATION and FEAR. Each should do it in privacy, so no one else knows about it or sees it. (Just knowing she'll do it might feel threatening to you, so it's better if she doesn't tell you whether she'll do it or not.)
The digestive tract analogy is a good one: Getting out the sh*t that's clogged in the lower bowel will get the digesion process moving again, but NOT COMPLETE it the first time it's done, so some other manifestations of grief reactions will show up, including dreams (which are higher power videomessages to help guide the dreamer thru the tunnel of grief to the new dawn on the other side). 2 more consequences are also likely: 1. one person's secret emotional turmoil hour(s) may trigger reactions in the other by psychic influence, because people who were each other's first loves can often have such strong unconscious bonds afterwards (LPC again, perhaps).
Did I mention that these letters, tho printed out, are normally NEVER sent to the addressee, nor are they showed to anybody else, least of all YOU. The writer may hold onto the script until it's burning a hole in her/his pocket, and then burn or bury it or both, whatever feels (symbolically) right. Yet some transmission may still proceed via ethereal channels. So one person's purging-expressing may trigger and foster the other person's.
2. The digestive & bowel-voiding events may seem to be getting out of the organism's control. And at that time YOU're in a position to advise either one of them to see their own counselor privately, because they are then doing grief counseling. There might be divorce counseling groups in your part of OZ too, but I'm not convinced that divorcees can show that much chaotic emotion in a group setting--you'd have to look into that.
"It's not your job," true, not in your Newhusband jobdescription. But your life is being cramped and jostled by their unmoving grief reactions, so you're supplying psychological laxative! I'm concerned that your wife may well NOT BE ABLE TO TOLERATE EVEN KNOWING that you're fostering her exhusband's healing too by subtly counseling him, and even by visiting with him at all. Perhaps your coaching efforts for her distant communications with him will soften her up to realizing that there are some ("viral") parts of the situation that you are best suited to handle. Nevertheless, it IS risky to set up a dual relationship for yourself (husband & counselor) and also Without either person's explicit permission. But people with counseling skills are likely to use them even when they "shouldn't."
And I think, seriously, that you CAN mention to each of them separately, that you had a class in grief counseling, and it reminds you now that their rapid-onset anger&outrage means their anger NEEDS expression, but in safer ways than by instigating snarling messes between them. It''s an "abstract conclusion that you're naively repeating" from a teacher you had way back when. (How does your wife get to accidentally marry a trained mental health counselor anyway?)
I can't spare the time to do this, but I'm glad that I did a little core-dump of how you as step-father can play a very influential role, if you utilize the counselor's ability to observe and intervene from an insightful distance. I expect you'd be least able to do that with your wife, because your own LPC is operative: but you CAN learn about what your unconscious expectations are by noticing when you're frustrated.