So here's what I think I would do:
Step 1: move anything you want to take to his new house into the household inventory.
Step 2: leave anything you want his ex to keep in the current apartment.
Step 3: Evict them together.
Step 4: Move them together into the new house.
Step 5: place the items you want him to keep in his new house.
Step 6: Move the ex out of the household and back into the old apartment, which you will purchase furnished so that all her old furniture is there.
No mods required; at most, you might have to do a money cheat to make sure both of the new households have enough cash for their respective homes.
