First, I'll answering your question with a question for a sec here: Why do people insist on getting in over their heads?
So, you married a guy who you knew already had kids. And now, after having another child together and cutting a day off your work schedule, you're on a tight, no-frills budget, with both money and time, for the foreseeable future.
Okay, I totally get wanting to have a child of your own and wanting a little extra time to spend with that child.
Beyond that is where you start to lose me. Here you're focused on digging in your heels and "refusing" go back to work that extra day, when that's not even on the radar for a couple of years anyway. While I don't necessarily disagree with the four-day workweek, I think your focus is a bit off here.
Because, at the same time, you're talking about having another child? Thereby ensuring even less money and even less time, and stretching the need for that extra day off further into the future. An additional child is a far heavier issue than a four vs. five day work week. And let's not forget, more tension, when your marriage is already showing signs of strain as it is. Piling on even more on top of this could easily lead to a break. And then you'd have far more serious issues than working one day more or less per week.
So, why not step back a little and at least consider not having another child and instead considering your stepchildren enough to fill that void? It seems to me the two of you already have plenty of children.
Also, you want (or rather, demand, going by your post) one day per week alone with your child but did you even consider if his children ever get a day alone with their father? They were here first and they deserve as much consideration as your current and possible future children together, not to be thought of as something he "owes you" for or somehow "not counting," as far as how many children you two have. An additional child's needs would also take more away from them, when they've already suffered loss.
Anyway, I hope I'm not seeming too rough on you right now but I'd urge you to re-consider how to best navigate so things get easier, rather than harder, in the future. I think you'd all win if that weighed in more strongly than an image you have in your mind of what your family "should" look like.
Also my opinion, as someone who's been married for decades, refusing/demanding and scorekeeping aren't great attitudes for a long and happy marriage. As a starting point, I think you're both far more likely to win if instead, you think of yourselves as what you really are now, a team where you both want the same main thing: The best life possible, all around, for your family (including the children he came in with). So that's my two cents, for what it's worth. Good luck to you.