Just for a moment - I'm going to imagine things from the point of view of the partner.
She's had the first days of a new, great relationship. The bloke seems great fun, poor thing's only got a crappy bedsit and his kid has to sleep at the foot of his bed like a pet. It's really expensive (maintenance, etc), so it makes sense that he moves into her home with her children. She looks to see if she can be friendly to the ex, as she knows it was very awkward at the birthday party, but he was insistent that she attended, as 'new family', etc, and there's been a bit of a lack of eye contact which felt uncomfortable, but she's not been able to find her. The New Partner says 'she must have blocked you'. Oh.
He's now comfortably in her house. Nowhere else to go, etc.
And he's drinking, but instead of it being 'well, I wasn't allowed to go out when I was with the ex, but you're different', there's a nagging worry at the back of her mind and perhaps a couple of times where she's not 100% certain whether he'd had a drink before driving the kids somewhere, but he's reacted badly to that.
He's been quite preoccupied with his phone. He's 'just' talking to his ex. So he says, anyhow. It's gone on for a while and she says something along the lines of 'well, you need to stop doing that, it's inappropriate if it's not about your DD', wondering all the time whether it's actually his ex or somebody else.
Every so often, there's something else that she's not quite comfortable with. When she says something innocuous, he reacts that she's causing an argument. There's a mention of Christmas decorations. When she says 'well, not really, I'm not keen on random stuff', he kicks off. Or he announces that the Ex has informed him that she has to decorate the tree with his DD's homemade decorations. No discussion, that's how it's going to be. Possibly when he already has a vague whiff of alcohol about him. She's 'starting an argument'. She's 'picking on him'. She's 'excluding' a child who she has welcomed into her home possibly too soon as he was only a new boyfriend, but he was maybe a bit too keen to move in and 'be a family', etc.
He's already telling her children what to do, calling her ex any name but his actual one, bitching about his ex's new partner and his age/appearance. He's not the 100% Nice Guy she thought he was. And he opened a can of beer up the instant he came in the door - coincidence - or is he trying to disguise that he had been drinking before driving? If she could be on good terms with the ex, that would have helped, as surely she would have said if he'd ever done anything like drink drive. But it's pretty clear from what he is saying that his ex doesn't like her.
There are reasons why you and him are exes. She may very well be finding out exactly what some of them are first hand.