Me and my ex do the whole amicable thing and he comes over at 6am on Christmas Day etc so that the children have a "normal" experience and Santa doesn't have to come twice etc.
We also do meals together for kids birthdays.
I have been single and he's with someone and I've always suggested she comes along but sometimes the kids say no and often she declines anyway. It's a quick get together for 2 hours or so.
This year we all had Christmas lunch together for various reasons and his family were visiting from further afield and of course his new partner came. It would have been strange if she didn't. I don't have that much to say to her but we can make general chit chat and share a bottle of wine with no issues.
One Christmas Eve I knew she was home alone while we were having dinner and I was adamant she should come along but she refused, which was her prerogative.
I feel for you, op, because if the ex gets a partner you'll probably be front and centre as she'll want her partner along too. Your partner should stick up for you but you could also suggest a meal on neutral ground ( for some other occasion, end of primary maybe? ) where you all go and break the ice?
When my ex got together with his partner I insisted on meeting her. It was the only stipulation I've ever made, but I wanted to know who was going to be around my kids so I could talk about her and reassure them I knew her etc. we had a coffee for maybe 45 mins and it was perfectly pleasant then she left and gave me a hug and it's the most we've ever really spoken but was really valuable.
Difficult maybe for you to suggest that but worth a try?