Shouldn't HE be the one making himself happy here if he really can't leave?
Look -- and this is coming from a single mother -- I feel your pain. I do. I'm not a native Midwesterner, I don't belong here, I've had a nice long rest here, but it could make you cry, what these people do with trees and buildings and landscape. I'm not passive-aggressive, I'm aggressive-aggressive, and the distinction is no longer amusing to me. And I've forgotten what it is to go to a decent museum just because you need to feel you some art. I'm also watching my daughter grow up without knowing the arts and taking them for granted, and this is not something that can be communicated later in life.
However, if I moved, I'd be moving her away from her beloved daddy and grandparents, and the entire world she knows. She's 5. There's no way I'd do that to her.
Really, as prison sentences go, it's not so bad. I remember thinking, when I was a young writer, that prison didn't sound so terrible -- you could knock out a novel or two, you wouldn't have to worry about making the rent or cooking, the noise might be a problem, the company might not be phenomenal, but on the whole you'd be mighty productive. Well, now's my chance. And that's exactly what I'm doing. Yeah, I still have to make a living -- more than before -- but as long as I'm stuck here for the next however many years, I can recognize that it's peaceful here, cheap to live, good libraries, decent people, on and on, and I'm probably more productive now than I've ever been in my life. Am I having a ball, no. Maybe eventually I'll figure out how to balance all this with having more fun, too. But I have this responsibility which I mean to carry out, so OK, and the truth is it's a good place for a kid to grow up. So's New York. It does leave your dh's kid in danger of being unwilling to live anyplace else later on, but on the whole the song is accurate. (Incidentally, I think this is true for half the faculty families I know, too. Most of the rest are probably just being polite. But most enterprising people don't really want to be here forever.)
If your husband is being a pill, he's going to be a pill anywhere. Honest, I've seen this happen, the New Yorker who leaves the city and proceeds to make everyone in a smallish town miserable for the next fifteen years, until he decides everyone around him is a hick and moves to a DC or Boston suburb. Let him take some vacations upstate, go pretend to be a lumberjack or whatever, go fishing. Just getting out of the city for a couple of weeks can help. I mean a good 200 miles away or more. Let him clear his head. But moving away from a small child...you really have to think back to what it was like for you, then, what a month was like, if you were even able to conceive of a month. Probably you weren't. It's an endless time. I recall that we say my paternal grandparents about once a month, and I'd forget their existence between visits. It was just too long to feel that they were really in my life.
There are others here who will say yes, we did it, the kid is fine. I would just point out, as others here have, that children can survive quite a bit and look fine in the moment. They'll cope because they want to be big and grown up and are proud that they can handle anything -- weren't you? That doesn't necessarily mean they're fine. At 6, even at 10, they're still very vulnerable.
So, long answer, but yes, making himself happy is your husband's job. And it's possible. Maybe there are less radical things he can do to get his head out of the city on a regular basis.
Good luck to you and your family -