Honestly op I suspect she's pushing for a wedding due to being a new mother, she was probably pushing throughout the pregnancy (understandable) but he's not keen. I suspect it's entirely possible he's told her its YOU delaying hence telling you "don't worry I'll sort it all". My ex pulled this shit.
If you want divorce sorted I'd recommend telling him to pull his finger out in a way/at a time that ensures that his new partner knows it's HIM delaying not you. That's what I did and within a few weeks things were finally shifting (I'd filed but he was stalling on signing/returning paperwork). It still does take time but you don't have to tell her that, and you never know it might go through quicker, my ex quibbled over EVERYTHING even bloody punctuation in the part where I stated reasons!
He did tell me ow was pregnant (bawled his eyes out on me to be honest - last thing I needed!) then to add insult to injury tried to make out she was less pregnant than she was.
Legally entitled or not, a decent adult tells their co-parent of things which have a major effect on their joint child. And a new sibling is a HUGE upheaval and toddlers are nowhere near mature enough to explain why and what they're feeling. You could've noticed odd behaviour in your DC and ended up wondering all sorts. He's a twat! And a selfish one at that!
I'd ask him if there's anything that as a co-parent he thinks he might need to inform you of? And if she says no I'd just come out and tell him I know. Don't need to tell him how (any number of ways you could've found out, sounds like you both live quite local to each other. Eg Certainly where I live all it would take would be a friend of mine who knew what he/she/they looked like seeing them in supermarket or post office with baby, news of a baby tends to spread fast anyway). Then say to him in a calm way that in future you expect the respect paid to you as his co-parent even though you're not together now, but you need to know about events that will have an effect on your child.
It doesn't matter that it was your decision to split, nobody goes into a marriage expecting to divorce, it's still a hurtful, tough thing to deal with. It's a type of bereavement and you've been in something of a limbo in the meantime. So don't give yourself a hard time that you're finding this difficult.
I can only speak for myself Re the "weird" feeling of ex having more DC. It was a reality hit thing, no turning back but also for me very hurtful that he went on to have more DC when I couldn't (medical issues). Personally for me it was a twisting the knife feeling, he was getting to do something with someone else that I couldn't do either with him or anyone else. It was me having to see him have the life with someone else that I wish we could have had. But everyone's situation is different. And yes the DC looking alike really doesn't help.
The feeling did dissipate though didn't go altogether. I've even taken his other DC for days out and babysat. Not for ages now though as he's other end of the country and no longer sees our dd.
I'm so sorry you're going through this its rotten!