Add me to the list of people who has always had a cat. We lived on a farm when I was a baby, so I was constantly around goats, cows, horses, chicken.... cats were the least of our worries!
I'm really sorry to hear about this situation you're stuck in, it just sounds like it could end badly for everyone involved - especially the poor cat. My DD has always been around cats too. My Siamese was intensely interested in Fiona when she first came home from the hospital - and why shouldn't an animal be? It's a new member of the family, it smells different and it makes funny little noises!

But my kitty's interest was just her mothering instinct kicking in. She was first to run to Fiona whenever she cried, and if I couldn't calm her quickly enough (like if I was making a bottle and it took a minute) the cat would meow at me to hurry me along and then even nip at my ankles if I didn't hop to it! It was pretty cute, and even now that Fiona is five, the cat always runs to her if she cries.
I've never heard of problems with healthy kids and cat dander, nor have I known anyone that had problems with their pets and babies. As a mother, I can totally understand that your wife is worried and concerned for the babies' safety, but - and this is a big BUT - considering that an animal's life is on the line here, she needs to take the time to research those concerns instead of hastily jumping to conclusions. That poor cat is part of your family. It's not the cat's fault that you had more children nor can she defend herself against any of this. If you can, put your foot down and tell your wife that you all made a commitment when you adopted the cat, and you need to keep that commitment and in time everyone will adapt. And they will, I promise!

There are always growing pains when a family adds members, be it babies or furballs. Once everyone gets used to the new routine it will be fine.