Could you be more specific on what you mean by a "three way relationship?"
The way it sounds to me is that A would move in with you and you would all be "one big happy family" but if your wife doesn't want another woman living in her house, then that's just not going to happen.
But that wouldn't necessarily rule out a "vee" relationship, i.e. you would be married to Z and in a relationship with A, but A and Z would not have to be bosom buddies.
Now you say that your wife is pregnant. I personally don't think this is the best time to be bringing this up. She's got a lot on her plate, she's hormonal, she needs to feel like the father of her unborn child is there for her 100%. I don't know when the best time would be, because obviously a newborn child will also consume a great deal of time and energy from both yourself and your wife, leaving less time and energy available for dating. But I've never been pregnant or a new mother, so perhaps someone who has been in those shoes could be more helpful in that respect.
“As I am sure any cat owner will be able to tell you,
someone else putting you in a box is entirely different
from getting into a box yourself.” —bisexualbaker