Interrupting Corrections

Hi! My kids, 8 and 6, regularly interrupt to argue during corrections. For example, "Just now I asked you to pick up the toys off the floor and you said ok, but you didn't do the task immediately. When you…" Child interrupts: "You never told me to do that."

At this point, I'm pretty sure it's not wise to respond, but do you just continue as though they hadn't said anything? I often pause for one second and put one finger up as my "that's an interruption" sign. Do you just keep going through all the correction? If I do that, they'll often just start ranting about how I don't listen to them and continue to argue their point. I suppose another option is to abandon the first correction and move directly to the second correction: "Just now I offered you a correction about not picking up the toys immediately. You interrupted which means that you were not accepting a correction…" But I see a lot of problems with that.

So I guess I'm wondering if there's a better tactic for the relationship than just barging forward with the original script. As I type I guess I'm thinking that if I keep my voice level down and don't raise my voice to match them, then I can just continue on. But I just know, putting myself in their shoes, that even if I'm interrupting someone, if they just keep talking without even acknowledging that I had something to say, I'd really dislike that. Is my question making sense? Would you normally pause the script to say something like, "When I'm finished if you want to disagree appropriately I'm really happy to hear what you have to say. But I'm going to finish my turn first though." ?

Any thoughts? Thanks!