Sounds like there is a problem in communication and in understanding. Maybe even with us here on this forum; we aren't privy to all that goes on inside your home. We don't know the dynamics, the finances, the space, the demands on the space that might be more important than your need for a dedicated layout space.... All we really know is that your wife wants your layout moved for the sake of your daughter's wishes/needs (not sure what's going on there), and that at long last you are getting a bit fed up with having to move every year or so. Maybe you need to look inward and find that line in the sand. People say "Happy wife, happy life." A marriage comprises two or more people, last I checked, which means they have to get along. Both of them. All four of them. It only takes one person to pee in the pickles, and its gender makes no difference. Just one partner/mate/bed buddy/spouse, take your pick, who is resentful will spoil the mood. Wife, husband,...either one can make a marriage miserable.
Taking things at face value, I gather your wife and daughter are unfamiliar with the basement. If they knew of the risks and ick factor that you describe, you can count on being looked at reproachfully for dragging your layout too slowly back down into the dungeon once they learn what you never made clear to them. You will be blamed for not informing them clearly what they are facing. Now is the time to sit down, all three of you, and for you to explain that you are getting a bit miffed at yet another relocation of your layout. Part of your ire will come, as you explain it to them in clear terms, because they are making a mistake, or merely ignoring facts you understand only too well. You must make it crystal clear why you have chosen to take the crappy space in the home and leave them to the warmer and drier places...for their sake. Explain that making the basement livable for a young woman is not going to be easy or cheap. For instance, it will start with a complete redo of the perimeter drainage, a project sure to cost about $8-13K. If you forego that project, count your basement's days numbered, no matter who is using it. If your basement goes, the house will follow. Now you only get the price of the land. It's value will fall because prospective buyers will know it has a high water incursion or water table. Problems for them if there were problems for you.
How am I doing so far?
Taking a deep breath, I could go on to suggest you make it clear that you will only move your layout one more time, if you must indeed move it, and that your firm resolve will be to finish it this time. Or, your other choice is to abandon the idea until the house clears of users...which may include the wife.
I'm just being realistic here. You have bothered to present a problem here over something that is sufficiently important to you that you have re-started it four times. FOUR TIMES!! Moving each time. It's time to deal with this household issue practically, honestly, and pragmatically. Think it over, find your bottom line, and present it to both of them. Be fair, be honest, be practical, and give as much ground as you can. Then turn into concrete.
Sorry, I can be long-winded.