The key is that all moves have to made in one session in Manage Worlds/Manage Households. The order doesn't really matter, you just can't to back to Live mode and then go back into Manage World/Manage Households to make more moves with the same sims. Please let me know if this is still confusing.
Just to be sure I understand...All eligible mover inners and mover outers must all be moved before any of the households are played? TIA
No, you don't have to make all the moves at the beginning of the game, but you do have to make all the moves for each household before you play that household. As an example, if you want to move Dina Caliente out, and you also want to play Don Lothario and Nina Caliente as a couple, you would need to move Dina out into a different house BEFORE you play the sims in the Caliente household. After you start playing the sims in the Caliente household, you cannot move anyone out. So in this example, if you move Dina, leaving Nina, Katrina and Don, and you start playing the household, then you can't later move Katrina out.
Regarding teens moving - No, they can't move as teens, but they CAN move after they become YA, even if you already played that house. Example - You play the Goths while Cassandra is a teen. Mortimer and Bella have twins and adopt a couple babies, and Cassandra is still a teen. You switch to another household to play. A few sim days later, Cassandra ages up to YA (while you aren't playing her). Once Cassandra ages up, you can move her out. She wasn't eligible to move out before you started playing the Goths, so you can move her out later, when she becomes eligible (in other words, when she ages up to YA). Meanwhile, Alexander ages up to teen and then later to YA - once he ages up to YA, you can also move him out.