Congratulations on the babies. That too would surprise me (declawed but not spayed....but I've seen it before )

Normally I'd say not to move them as mom might try to take them right back where SHE wants them. But when they are in danger (like out in the wild) we would move them to more suitable quarters. I think your move will be fine. Give her a choice of beds because she may like to have them in a different spot . (no accounting for a cat's taste, you know)

When do you think you will be able to get pictures?

Oh yes, are you certain that there are not other babies? Look thoroghly, I'd hate to have them die if there are others.