Oh wow it’s all very quick isn’t it?
I find it hard to believe this wasn’t the other women during your relationship tbh, has he admitted to cheating?
But I suppose that’s not really the issue now.
Honestly it’s far, far too soon to be introducing anything be to anyone. I wonder why he is pushing for it so much?
The children need time to heal and learn that their daddy still loves them, they will always be no.1 to daddy and his new home is their home too. This all needs to be done without the new partner so your children adjust to the new situation without feeling pushed out and no longer loved as much by their dad.
He needs to make sure they understand that he may not love you like he used to but he has spilt with you not them and he still loves them just as much. He cannot do this while introducing a new woman into the mix.
As for the living situation, it’s awful he hasn’t provided a home for his children where they can reconnect with their father without another woman being there. It will make them feel quite insecure I imagine and very unlikely to ever feel like it’s the home they share with their father.
It gives quite a lot of red flags that the new partner is happy to be introduced at this point. I cannot see it being a harmonious step parent/partner relationship if she has such little empathy for how the children will be feeling.
You cannot do anything about him introducing them, he has a right as their father to do as he wishes (within reason) BUT introducing them so soon and not providing his children with a separate home they feel is their own where they can re-bond with their father makes him a rubbish person and a really rubbish father.
This is not going to end well if he carries on in this way.