The house being from the Exchange can definitely be part of the problem, maybe all of it. They can be very glitchy. Also, a couple of things to try:
When a Sim is stuck, try resetting him/her. Open testingcheats window and type: resetSim Firstname Lastname. It's case sensitive, so be sure to type it exactly like I've shown.
Another thing with the furniture spinning instead of moving into family inventory, you might be trying to click and drag the furniture by holding down the left mouse button. To move things to the family inventory, you click it once, put it where you want it to go, then click again to release it. If you hold down the mouse button, the item will spin because you're rotating it instead of moving it.
I hope this helps!