How about this:
If it doesn't need to placed on the lot when you buy it, it doesn't count. Therefore, reward cars don't count - both from careers and the motive mobile, and anything that doesn't get placed on the property doesn't count, including the collection helper and moodlet manager. If you need to place it to use it, then it counts, but if you can use it from inventory, it doesn't count.
Your sim can take their 4 items from one house to another if they want to, but only 4 items can be left in any one house. So if you take all your items, for example, and you get to your last house, you can still only leave 4 of them - the rest must remain in your sims' inventories/family inventory.
Would that make it simpler?