There's actually more to this story. Back in late 2014 or early 2015, I first found out about FIRE and was instantly hooked. I see that my first post on here was in January of 2015. I tried looking for another Mustachian to date, but did not meet one. I started dating my husband shortly afterwards. He was frugal compared to most people. Our first dates were either free or cheap, and we split the bill. For example, we went hiking one time and ate at Panera another.
I told him my FIRE plans within a few months of dating, with exact financial targets for my goal of retiring in my mid-30s. He said he was not interested in joining me in FIRE, but would support that goal so long as I would take care of any kids. That seemed fine. Now after detailed conversations with him, I realize he was going along with my plan in a "we'll see" way. I've been talking about it all year long, but he thought it was merely me venting about my job instead of being serious.
My friend says I should have gotten the 2015 agreement in writing.
It sort of sounds like both of you saw a major potential conflict but didn't want to lose the relationship, so you found a bandaid that you both were willing to look at as a solution, and walked down the aisle.
He never really wanted you to FIRE, and you never really wanted to be a homemaker. (I'm guessing that "take care of the kids" probably meant more than just driving them to soccer and overseeing homework. Especially since in previous threads, you've talked a lot about division of household labor. It seems he meant "be a homemaker and housewife, so the vacuuming and dishes and Christmas shopping and cooking are yours". That's what a lot (I'd wager most) people say when they sum it up a "stay home with the kids". Any woman (and a couple men) I know who "stays home with the kids" phrases it about like that, but does all those other things as that's usually the role of the SAHP. So I'm guessing that's what your DH meant. And it sounds like, if you said you'd stay home with the kids and pick up the majority of the household and emotional labor stuff, he'd go for that, even if he didn't get his third kid. He does most of the cleaning now, and probably feels that if you are staying home, you should be picking up most of that, not just taking care of the kids. But you don't want that. (which, to be clear, is completely reasonable and understandable, but so is him not wanting to work FT and still do 50% of the house stuff. So neither of you is wrong or unreasonable, but your stances put you in opposition.)
So I'm not sure that getting it in writing in 2015 would have helped, unless it made each of you get more specific about what you actually wanted, meant, and were willing to agree to. You have been on fundamentally different pages about this stuff since a few month into dating, and kicking the can down the road for years. It sounds like you saw a friction point in your relationship and were worried about what would happen it you icked at it, so you came to a vague, rushed agreement on it so you could avoid a potential rupture.
I agree with MC that he doesn't seem to understand what you actually want. Do you understand what he wants? If he were posting in a message board somewhere with his version of the story, what would it be? Other than the "third kid" thing, he actually seems fairly reasonable to me. Just a different version of reasonable than yours.
What is the compromise? What's the middle ground for you? Usually that might be something like part-time work, but you've [both of you, from the sounds of it] have made the nanny a non-negotiable in this, which you say takes that option off the table. Once you dig to really understand his motivations, what can you do to move in that direction, partly, that doesn't entirely disregard your motivations? What can you ask from him that moves you closer to yours, but doesn't pull him too far?
As a side note, if I ever got to a point with my spouse where I was thinking maybe I should have gotten something in writing, I'd be terrified about the state of my relationship and getting into counseling ASAP. (Yes I know you said "your friend" says it, but you wouldn't have mentioned it if you didn't see some truth or value in it.)