Does the impurity transfer from a dry impure object to a pure object if a wet pure object touches it several times in close succession, and are the house and family considered impure because of that?

You have been severely afflicted by obsessive doubts (waswas). What we advise you to do is to completely disregard these doubts and pay no attention to any of them. The mere contact of an impure garment with a pure garment does not necessitate the impurity of the pure one unless you are certain that the impure part of the garment touched the pure garment while one of them was wet. As long as you are not certain of this, impurity is not deemed to have transferred, because the transfer of impurity is not ruled by mere doubt.

Some scholars have held the view that if an impure object touches a pure one, and one of them is wet, impurity does not transfer, regardless of whether the contact is repeated or not. As long as you are afflicted by obsessive doubts, there is no harm for you in acting upon this opinion until Allah Almighty grants you recovery.