It is absolutely true that pit bulls are fundamentally good dogs, and their bad reputation comes from the kind of people who often choose them for training to be vicious guard dogs or "drug lab protection" dogs.
HOWEVER... pit bulls are huge and very strong; a single snap from their jaws can be fatal. That's why the drug dealers like them. And like all animals, pit bulls sometimes surprise us with a sudden instinctive actions we could never have predicted. For these reasons, I think it's dangerous to have a pit bull, or any large dog, around a baby. The stakes are just too high to take the risk.
Having said that, let me add that I once saw a beautiful little boy about 18 months old in a store with his mother, and his face was covered with long red scars. I was too shocked to hide my reaction, so I just went ahead and asked her what had happened, and she said, "It was a cat."
So. These things do happen, and of course, your baby is your first priority. For what it's worth, here's my suggestion:Option 3:
(a) Let the dog live in the back yard, with indoor visitation rights under the supervision of his "dad," so he isn't roaming the house and making the cats nervous. Once the baby comes, allow indoor visits only when both parents are present -- one to hold the baby at a safe distance and one to keep a very tight grip on the dog's collar.
(b) Equip the cats with SoftClaws, install a couple of Feliway "Comfort Zone" diffusers in the apartment, apply catnip to their scratching posts, and try to give them more interactive playtime with you -- not a long session, but several short ones during the day. By the time the baby arrives, you may see a significant improvement in the kitties's behavior.
(I know you said the cats were wacky even before the dog arrived, but without the dog's influence, they might have settled down by now.)
(c) As a last resort, if things still aren't working out... find good, loving homes for some or all of them, and don't adopt any more animals until you're sure it's "furever."
I wish you a healthy baby and a happy resolution to these issues!