Do your DC want her there?
I read your other thread. I think at some point it's got to stop being about you, or her and your exH.
It's great that your children know you and their dad can still get on and be friends and you can all be together for big ocassions. But, for your children's sake, you need to start looking after them separately. If she is there when they are with their dad, so be it. Even if she does try too hard to win their affections, so what?! You are their mother and their primary career and therefore irreplaceable.
With the situation as it is, YNBU not wanting her to come to the party. Especially after only six months.
But if this is a long term relationship, it's going to happen eventually and you need to get your head round it.
My ex hates my DP purely because he loves with me and our DD. Because ex feels so strongly DP didn't attend her recent birthday party. It wasn't an issue and TBH I would have been pissed off if DP pushed the issue as it would have made a happy day tense and horrible.
BUT...when she was in a nativity at Xmas, I insisted he came. Because she was so excited and she said herself she wanted him to come and watch her. She'd have. been gutted if he didn't. ExH was spitting feathers but we all attended and DP did the decent thing and slipped off at the end of the show and told her how awesome she was when she got home.
I'm hoping this year will be easier and DP might even be able to attend her party without a fuss.
Your ex's new GF is pushing too hard but he is being weak and shit not drawing any lines and feeding all this back to you.
I'm not surprised you feel pissed off but it's him who is handling this wrong, not her. You might have to accept that if she is a long term fixture, the DC will eventually see her as another important adult in their lives.