From what I can tell the sim who gets the bulk of the household inventory is whoever is left in the house. Basically the last sim in the house.
I split my household last night into two families. It was the first family that got to keep the household inventory, money and house.
However, this was when I used the evict option. I haven't tried the move by phone/computer option.
Moved out the 2nd family via the phone and it looks like they split the household cash and ended up getting the family inventory. The first family got to keep the house and what items were placed.
When I tried the kickout option all the 2nd family got was half money and no family inventory.
I'd also like to hear what
@Schipperke has to say.
MrsFlynn