Caring is ACTIONS.
He did not care for your SN child, his baby or you when he abdicated all actions of parental care when he lived under your roof.
He selfishly came home and played computer games and fought with you like a truculent teenager.
He did not actively care for his children. He did not work with you to support you in this momentous 24/7 challenge of your SN child. He sabotaged your efforts, he fought with you, ridiculed you, he emotionally abused you and gas-lit you around your MH.
He drove you to distraction. He did not support, cherish and care for the mother of his DC - or put in any direct care for them. And by his actions he has left them with a depleted, diminished mother.
That’s what makes him a deadbeat Dad.
Yes he can rock up for a couple of hours on a Saturday after a week of the single life, 100% responsibility free, ego nourished with his career and of course he has the energy and the focus to be Disney Dad (look that one up) - and of course your DCs will be delighted to see him.
But you know his contribution is no more than a children’s entertainer. You would have less stress employing someone to make balloon animals for a couple of hours - at least you wouldn’t get sexually harassed, emotionally abused or manipulated 24/7.
He drove you to distraction when he was living under your roof - you did brilliantly to get him out and you have moved mountains for your DS. But this is really hard work to sustain, you need every drop of energy - for yourself and your DC. Stop letting him rob you of this and still sabotage your life from a distance.
If you are sorted with the school look to invest in respite - there will be professionals who will help your DS adapt and transition slowly. You all need this to survive.