So you've been together a year and already live together? That's pretty quick moving for someone with a young child who wants to put that child's interests first.
My ex moved in with his new partner very quickly too. I'm sure she thinks she knows the ins and outs of our situation, just as I thought I did with his previous "crazy" ex.
Police put a restraining order on mine for coercive control. He wasn't allowed to contact me directly or indirectly. I refused to give him my new address, but he found it out anyway. I still don't know how as I know family and friends wouldn't have given it to him.
When he moved into his current house with his girlfriend he refused to give me his address saying I could find out where the DC were by installing life360 on my phone (meaning he'd be able to track me as well). A family law solicitor told me whilst ever I had parental responsibility I had a right to know where the DC were staying in case of emergencies.
Anyway, they are older now and DC themselves have told me his address. I never approach the house to collect them, I park around the corner and then phone them to come out.
Please don't assume the picture he has painted off the story is the full story. Yes, some parents are malicious and use parental alienation to get back at the other parent to the detriment of their kids.
However, regardless of who is right or wrong, the situation is toxic and it will be the children that suffer in the end.
Personally I think you're being given a very one-sided view. It would be interesting to sit down one on one and have a chat with the ex-wife as to her version of the story. Why wouldn't you (and why would she refuse this) given you are going to be taking responsibility for her child.
I'd be more than happy to meet and chat with ex-h's new partner, though she's not interested in our DC.