Protolawyer, I'm sorry about the proposed move.
On the other hand -- welcome to having children. And that loss of control isn't just to do with stepchildren. Unless you go to a sperm bank, there is always the risk of your husband divorcing you and filing for custody, of having to move or give up careers to stay near your child, the involvement of courts, the hostility of grandparents, and the appearance of stepparents you don't know when you have a child. These things happen depressingly often. Having children means ceding tremendous control over huge parts of your life, even when the children are healthy.
(And had I mentioned school? Yeah, control, not so much.)
All that said, I think you guys do an incredibly tough job. I have no intention of remarrying while my daughter's under 18, but even later on, I don't really want to deal with a man's children. Their parents are bad enough. Their grown children would have to be solvent and exceptionally nice, with sane spouses. I won't even go out for dinner casually with divorced men who start telling me about their children. I don't want to be involved, and I sure don't want to meet the kids, even as an honest-to-God friend.
About money and whose it is: Both child support and most of the money I earn are for my daughter. I maintain this house, yard, car, lifestyle for my daughter. I sure don't need it; I used to live happily on about a third of what this life costs, but a scroungy writer's life in a tiny apartment with no play space and a crummy local school -- not so good for kids. General savings are for her summer camp, music lessons, trips to cities with decent museums and theatre, her inevitable expensive career (please, please don't be an artist), plane tickets to visit relatives I'd quite happily lived without seeing for years, and other extras that may do good things for her. The money I save in college and retirement accounts is for her. The college money so she isn't crushed by debt the minute she walks out of school; the retirement money so she isn't obliged to support me when I'm old and she's trying to take care of herself and her own kids.
People aren't tremendously good with money in general, so it doesn't surprise me when they marry and have children without thinking the money through carefully. But it does seem to me that if there's any hint that you might resent the state's counting your income towards child support, you shouldn't marry a guy who owes it. Live with him, do as you please, but don't oblige yourself legally. No good can come of it.
If your state doesn't count your income, of course, then it's probably wise to view yourselves as being independent people incomewise, or to understand up front that he's poorer than he looks on paper, because he has a prior longterm obligation. So he pays it out of his own income, and the rest he puts into your family pot. If you begin to look at the child support money as "that should be partly mine" (which is what you mean by "ours"), you're going to be unhappy. Understand ahead of time that you're marrying a guy who's got a 10-, 15-, whatever-year income reduction, just as if you were marrying a guy with tremendous student loans, or a guy who works a poorly-paid job. The income isn't and never was available to you or your family with him. It's what he owes.
That's true even if the ex-wife has enough money to take care of the child herself and then some. If I were suddenly making enough to cover everything, I'd put that CS away for dd, and then she'd have a fund for grad school, house down payment, health insurance post-college, whatever. (Many single mothers do just that.) The father's financial obligation to the child doesn't go away just because the mother can carry everything herself, or has married another man. That's an ethical matter as well as a matter of law.