I live with the Father and have 2 kids (baby and nearly 4). We have a big place, and I have a room for camming which is at the opposite end of the house from the living room. I go on nights, but my partner and I have the deal that if he does the majority of the childcare, I pay the majority of the bills. He works a little and goes to school too, but he does things where he sets his own schedule. His classes are all online, and basically, he takes the full-time childcare role. It's old-fashioned, I actually don't know anyone else who shares finances with their partner anymore, but it works for us. Our rent is astronomical and food bills per month are really high too, so we've had to strategize.
With breastfeeding, it is a bit difficult because I'm up a lot through the night, but we make it work, and supplement with formula when I can't manage a feeding.
Since he's doing all of this and putting his own career ambitions on the back burner, I'm also the one who will be buying a house, even though it will be in both of our names.