Hi OP, when I saw you'd updated I really hoped that the reason you hadn't posted was because everything was sorted and you were either happy in NZ or back in the UK. I'm sorry to hear that things have been so tough for you, but it's great that you now have proper support. Sad that your husband is showing his true colours, but given how long he's been gaslighting you and suggesting you are the problem, there must (?) be at least some comfort in knowing that you weren't the problem?
Also, if he's only seeing the children a few days a month, he's not going to want to ramp that up to 50/50, but presumably your worry is that he'll take the time and palm them off on his ropey family? I'd say that if he hasn't tried that already, it's fairly unlikely?
All the best to you - I've though of you often over the last few months.