I actually believe that what some people who finally "emerge" from MLC say, that they felt like two different people or like they were watching themselves. (An observation from my friend who had postpartum depression as well btw.)
I remember one time last year, we went to a therapy meeting. My then-H and I were having a conversation and I said perhaps we could continue it in the car on the ride to pick up our son from school. He panicked and told me that this was a bad idea for our son, all the while, clearing out space in the passenger seat for me. I ended up not riding with him, but this struck me as odd. Since reading about the split brain I have wondered a lot about this.
My feeling is that for this reason all communications are best kept to a minimum and directed if possible at the children, not the MLCer. The other day my former H had our son pick up flowers for me because I was sick. I texted a thank you to our son. At this point, I think it is humorous in a way that I need to make sure that he knows that I know that we are "over."