Let's be sure I understand correctly:
1. Before moving to a new home each Sim is allowed to leave no more than one unique object purchased from Buy Mode; i.e. no reward objects, planted items, hand-crafted items or found objects may be left behind.
2. Each Sim is allowed to purchase two items before the first move that they can keep permanently; i.e. any later purchases that aren't being left behind must be sold before the next move. Or are no new purchases allowed at all?
3. Reward objects, found items, hand-crafted items etc. not purchased from buy mode must be carried forward so as not to run afoul of the restrictions on household income.