I think the term "back-up" needs definition.
My DW spends a good deal more time in the presence of our children than I do. She is the on-the-spot disciplinarian, and I think this is a role that many, many mothers for centuries have found themselves, primarily at the youngest ages, perhaps less so as the children get older.
She starts training them in obedience from the time they are nursing. When they hit 1.5-2 yrs, and start throwing a tantrum, they start getting the rod. Now, if I'm around, I will make on-the-spot corrections, and discipline if I have to. And we try hard to be on the "same sheet of music" so that the children don't get mixed-signals from each of us. We try to have consistency.
But in all truth--when I have to do a paddle, the children know that they do not want to get a paddle from daddy, because it is usually more "memorable" than from mommy. Not that mommy does her discipline with a feather-duster, or anything like that. But she has her way, and I mine. And I'm fine with that. If she calls me in, it is usually because she has reached a place where she 1) doesn't want to snap, 2) has too much going on right then to do justice where it is due, 3) may have already paddled one several times. The dear child knows it has graduated to a new threat level.
This, to my mind, is not so much "backing-up" as teaching a kind of "chain of command" principle, and gradations of wrath. When I'm at home, if I see one stamping the feet or flouncing, I act immediately to eliminate that behavior. My DW, will occasionally tune out certain "lesser forms" of that behavior if she has half a dozen plates spinning in the air, praying that 1) dear child will wise up and back out of that mode on its own, or more likely 2) child escalates to "intolerable" / "can't ignore it" and something has to be done. I am the HEAD disciplinarian in our home. I'm just not the PRIMARY disciplinarian, during most of our dear children's young lives.
We have a system. We have a fair degree of harmony in the house, In my humble opinion. Usually, by age 3-4 we have achieved a certain degree of docility/compliance in each of our children, so far. And they are a joy when they so want to please.