So, his position is:
Your sister confided in him and trusted him with secrets about her behaviour in the past, of which she was ashamed and didn't want her partner to know.
When she found out about him having done the same thing as her - only to you - she came down on him like a tonne of bricks. She betrayed his trust, in his eyes. He couldn't trust her in the way she had trusted him, so he broke her trust and told her partner her bad secrets.
In his eyes, what he'd done was no different to what she'd done. He felt that in the same way that he hadn't judged her, she shouldn't have judged him.
Now, let's work out what's wrong with this - because what is wrong with it is what makes everything so painful and so unviable.
What it might be helpful to think about is: he feels everyone is judging his betrayal of you, and he wanted your sister's betrayals also to be known about, so he would be seen as someone who's made a mistake, but can be forgiven for it. That's what's driving this - his desire to clear his name, effectively. That doesn't make it right, but it does understand his absolute insistence. Asking him to apologise is, to him, asking him to say he's more guilty than your sister - and that's what he can't swallow.
What's wrong is he's failed to take on board that you are her sister, and that his was current behaviour, not past.
He's made the mistake of thinking her trust would trump her feelings for you.
He basically didn't think about how much she loves you, and that in turn shows how he still hasn't felt how much he's hurt you.
He hasn't thought about how much he's hurting you in trying to make you choose him over your family.
He hasn't thought about how much he's hurting you in using your little boy and your commitment and desire to seeing your nan in a pincer action.
He hasn't thought about any of this. I think because he can't - because he is missing a chip. And that chip is the vital one - the difference between a gentle, happy life for you and your son, and a miserable, painful one being tossed from one unbearable emotion to another.
...
What you need to let go of is:
the hope and quite strong underlying belief that it is better for your son to be brought up with his father and you than with you separated, and maybe with other partners.
And:
the trust that ultimately he must love you as you love him.
...
What you need to really grasp is:
although of course in an ideal world we will all be deliriously happy, the first person to consider here is your little boy. He is utterly dependent on you both, and he only has one moment of being each age that he is. This is his childhood. This is it.
And it will get worse if you stay together.
And even things which you might not consider as high stress for him - such as the business today of where he was going and if he's going to his nan's - and possibly catching on that you're upset or at least stressed - these sort of seemingly low-risk exposures to stress do in fact have a very strong and negative cumulative effect on little ones.
So you need to act sooner rather than later.
It goes without saying that it will be better for you, as well, to get out of this situation. It will take its toll on you as well as your son. It will, over time, really degrade your life. And you too have only got one moment of being every age you are.
...
I think that if you're strong enough, just calling time is best. But you might need some moral support to do this - you might need some counselling or other support.
But your main task is:
Understand that you have to do this. Be strong for your son. Protect him from this harmful situation by ending it.