You were looking for a reason why he left. There's the reason.
Less than 2 months since the 'I'm not happy. I'm leaving' declaration. And now he's comfortable enough to include the OW in the very little time that he does have with the children. He feels that enough time has passed and that everyone will fall for the 'we only just started seeing each other' line.
All of this planned out.
He said he'd been unhappy for a year? That means that he's been seeing her for a year.
And of course that's why he hasn't got his own place yet. A single man wouldn't see a future for himself and his kids in his dad's small bungalow (where the kids don't even get a bed) and would make plans to move.
A man intending to set up home with his new girlfriend would stay at his dad's for a short while, 'suddenly' strike up a romantic relationship with an old friend and then get a new place with her. Or move into hers. They've been planning this for months.
Well, he's made a big mistake, hasn't he? He didn't sort out his finances with you before he brought the other woman into the picture. And now you have no incentive to play nice with him. No more 'poor DH, can't afford a nice house for himself'. Looks like his plan all along was to end up in a nice house with the OW with both of them sharing the bills. And once he has a nice large home then he might want 50% residency of the children so he doesn't have to pay the maintenance that he said he would pay.
Be really careful, OP. You have to be smarter than him right now.