I think I've mentioned this before, but there are a lot for forums online for dads in the UK going through divorce. You might be able to get more relevant advice as to how our system works and also speak to other dads going through the same thing. Our system here in the UK, I am led to believe by friends who have divorced, tends to favor the mother in determining the custody arrangements so there would be a lot of men going through similar difficult custody battles.
I have to admit I do not understand your W. I understand (to a degree) a WS/WAS who abandons both their partner and their children (part of the escape responsibility fantasy) and I understand a WS/WAS who abandons their partner but, once they've left, suddenly fear losing their children and double down on being a good parent, but I do not get someone who very obvs. has no interest in being a parent (a real parent would want to minimize the impact on their kids) but fights dirty (incl. using the children) to keep them. How can she be so petty that she would fight for something she does not want just so that you can't have them.
However, her motivations don't matter. In the end, the only thing that matters is how you deal with it. And it sounds like you are dealing with it in as dignified way as you can given the circumstances. Keep strong. Don't stoop to her level and FFS start keeping a journal of dates and times and things that were said. Also, I agree with Twofeet, I would fight to my last penny if someone tried to keep me away from my kids. Houses, cars etc are just things.
I would urge you to do a quick google search on UK divorce resources for fathers. Our system is not the same as the US.