EX Wife hates my current partner - we have kids and it's becoming a problem

I'm 28 and my ex wife is 29. We were married for 4 years (together 6) before splitting up over 18 months ago, we also have 2 gorgeous girls (aged 5 and 3). Things were really messy during our split but have settled down. Neither of us were particularly happy in the marriage and it just exploded. I feel like we're both happier people now and we actually get along and have a laugh and can share special events with the kids (birthdays/random beach outings etc) - it's really nice.

Problem is I've been seeing someone for the last 6 months or so, and she is someone my ex-wife was friends with in highschool but fell out with not long afterwards. This is causing huge problems as my ex wife does not want her around our children, or to even meet her again or have her at events. My new SO has 2 children of her own as well around the same age so it makes things hard when they are excluded from events with my children. The way my ex wife was during our breakup (she lost the plot, used the kids as ammo etc) makes me cautious about how to approach this, but I'm really at a loss as to what to do. It would be nice if we could all hang out and get along (ex wife has been seeing someone as well) but I know that will never happen as my ex wife hates this person. I'm not asking for us to be one big happy family but it would be nice if we could all just get along. She's even said "if it was anyone else I wouldn't have a problem with it."

I'm not about to give into my ex wifes demands here, but I hate that this may turn into a huge problem in the future. Do I tell my ex wife to stick it, or just suck it up and realise it will always be this way?

TLDR: Ex wife hates my new SO and refuses to let my kids and hers socialise or even treat her with any respect at events for the kids.