Good grief, it is NOT ok to bring your child into this. There might even be negative legal implications to doing such a thing. Get that thought out of your head. It is enough that she sees behavior between you and your Wife. It would be highly inappropriate to have your 12 y.o. daughter give you commands or even think she could. She is first and foremost your child.
However, she will at some point discuss this with her friends and see how their parents interact and see it is completely different from her own household. At that point it is likely she will become confused and conflicted. At that time it is up to the two of you, your Wife and you, to calmly explain there are different ways that families work together and this works for you guys. You don’t need a lot of details at least at the get go. When she gets to about 25 y.o. is the time you – and more importantly your Wife – can tell her more about how things work, if she shows an interest.