I knew it'd be two sons as soon as I read your post and saw that your ex was a lazy entitled twat.
Teenagers don't need much of an excuse to hate/pull away from their mothers, and your ex obviously didn't value your work ethic so why should they.
He's been dripping his side of the story into their ears for over three decades, he's had all the time in the world to do this, while you've been out working. Teenage boys often hero worship their fathers as it is, and that is the example of manhood they will either follow or reject
Unless you really did abandon them - which it doesn't sound like you did- then they really do need to grow up, but they probably won't
It doesn't sound like the issue is with your partner per se, it's because his presence threatens your long held family position as cash cow and holder of the purse strings. That's why they're up in the boughs at a threat to their inheritance.
At the same time they can take the moral high ground over "a mother leaving her children", so they're nicely situated to blame you for everything they fancy, for the rest of eternity, and never analysing their father's role in how events played out.
My parents actually split up and got back together when I was younger. As well as that, both occasionally missed school events because of work. I wouldn't dream of holding it against them somehow. I'm about the age of your DC and would be utterly mortified at myself for the sort of behaviour they're showing. As a working mother of two children, frankly I wouldn't have time to police my mother's life the way they do yours.
I think if they're acting like toddlers then treat them as such. Ignore bad behaviour and attempts at manipulation, keep your cool, reward positive behaviour. Have the conversation about their childhoods and the decisions that were made in a calm way and be careful not to appear as though you are blaming your husband - just state facts and mix them with a bit of reminiscing, you know "from 1997 to 2005 your father did not feel able to get a job, so I had to up my hours in work to cover the mortgage. I was very upset at the time as I felt you boys were still so young, but I had no choice. I remember feeling awful because I missed your Harvest Assembly in 1999, but I was pleased your father could attend at least, apparently you were a wonderful carrot, Joshua"
I think if you're calm and open about it, it might open their eyes a little. They need to realise you're an adult woman who made whatever choice you thought best at the time, and get out of the "daddy said mummy can't be bothered with us" emotional rut that I reckon they're in.