I'm so very sorry you find yourself needing SI--but am glad you found us.
Regarding the marriage, you do not have to make any decisions today, tomorrow, or any time in the foreseeable future. You can stand back, and see how things unfold. (This will, incidentally, require some action from your husband; his passivity is worrisome.)
Right now, you're thinking in HUGE absolutes: "crushing our dreams and moving to a cramped apartment." There are in-betweens.
That said, the new house concerns me. Given the magnitude of the infidelity (and the "punitive" nature---that you were "warned" suggests, to me, that you were set up; "lack of sex life" is two-sided, and some people ....arrange their sex life at home to FIT their adulterous intentions. Your husband's "warning" that he was going to cheat, and his passivity and lack of remorse in the aftermath of discovery, make me wonder if YOU were set up.)
I would NOT purchase a bigger house with someone I'd just learned had betrayed me.
If you want to try to reconcile, that's fine---lots of us do, and many of us succeed. But it's a lengthy proposition, and it can be a few years before you know if it's even possible.
In your shoes, I'd withdraw the house from the market. You don't have to move and, in fact, the market is improving in many areas of the country such that you might do far, far better in two or three years.
If the offer you received is stupendously good, I might accept and sell---but I would NOT buy another house. Not now. Not with man with whom I was not absolutely sure I was emotionally safe.
And no matter what words he tells you (and they sound pretty crappy right now, with his "I warned you" garbage and his reliance on YOU to clean up his mess), you will not know where you stand for quite a while.
If he's committed to reconciliation, he won't have any problem with you taking half the proceeds of the sale of the house and stashing them in an account he can't access. No, you won't access them, either---unless you NEED to.
My point is this: this man is a stranger, and your marriage is over. Whether you will be able to build a new marriage with him remains to be seen. He may become remorseful and completely committed to the marriage, and you may do really well. He may become completely committed to the marriage, and it won't be enough. He may remain an, "I'll do whatever you say, but don't count on ME to do anything to fix this" guy, and never prove himself suitable for reconciliation. And you won't know ANY of this for, quite likely, at LEAST many months, if not years. (I can't count how many of us believed ourselves to be staying with partners committed to reconciliation who were, in fact, still cheating.)
If you can't stay put, then rent a house. No, it won't build equity----except it WILL: it will build equity in your marriage. That's a small price to pay for the opportunity to prove that he's worthy of a lifetime with you.
Meanwhile, you will have have---safely tucked away---half of the proceeds of the sale of your current house. That way, you will know you will be able to set you and your kids up comfortably, if need be. This is NOT a plan for reconciliation to fail. To the contrary, it gives it the best changes. You will be there by choice, not necessity. That is powerful, for BOTH of you.
His passive, "I'll do what you say" doesn't really speak to real remorse, at this stage. That doesn't mean he won't get there---but I'd be very, very reluctant to make any more life-altering changes with him, until the fallout of this his decision to cheat is thoroughly cleaned up.
ETA: Another thing to think about: his affair was with a coworker. Often, the only way for the BS to feel safe in such a scenario is for the WS to leave that job. So, factor that in, when considering purchasing another house. Right now, it may seem tolerable for him to continue with the same employer. But triggers can be fierce, and that can change at any time. I'd want to choose a house I could pay for comfortably on one income, if need be.
[This message edited by solus sto at 9:22 AM, June 25th (Tuesday)]