Oh aleC I am sorry that yet again he's told the kids in this way. What a selfish man. I think your kids will be fine and you will be fine.
You can assert yourself and not let your kids be more involved with OW and her kids than they need to be. They're just getting used to dad not being at home, seem to be coping well, and now he drops this bombshell. He, like so many others, chooses to focus on his happiness at the expense of his kids.
Be assertive and strong. Let your kids lead; if they don't want to stay overnight, then that's fine. He will rush now to have a perfect 'blended' family, which he has been picturing for months. Doesn't mean your kids want the same, so continue to put them first.
You're their mum, their constant, reliable rock. Don't underestimate that, and don't for a minute think he and his new relationship can diminish your relationship with your kids. He can't. Listen and respect their needs.
I repeated this to my kids in the first years post break up: 'Only see your dad because you want to see him. Never see him or stay there because he wants it and you don't'. Mine were older, so I appreciate we had no agreed access, it was entirely up to them, but yours are at an age where their feelings must be taken into account.
What a sad stupid man to throw you and your kids away. Another walking cliche, so bloody predictable.
Stay strong.