You can split Households without having to move them in with another Household.
You can use their phone. Under Travel - on your Sim's phone - select the "Split from Household and Move" option.
This will open the Household Management dialogue and you can proceed from there.
You can also split Households directly in Household Management.
Select "Create a New Household"
This will create a new household, but they will not be in any world.
Now, you can move them wherever you want.
Wow! I really appreciate how much you put into this. Truth to tell, like I said, I literally tried everything from Managing Households, to the Phone (Home and Travel, because I figured both had a chance of being a feasible option), to clicking on the Sim. I didn't have that option for anything. I'm sure I've split households in all the years I've been playing TS4, although I don't do it often, and thought maybe the problem was because it was an apartment - I don't have "For Rent", though.
I ended up saving the "family" to the library, then plopped them into the other apt, then deleted the Sim I wanted gone. Because they're just mostly unplayed Sims that I wanted to "fix" for interactions with my played Sims, I wasn't too concerned with whether or not I maintained relationships, funds, collections, etc.
Hope that if I have to do this ever again, I am more successful, LOL.
