Since they both report to you, can you address it now (verbally) rather than waiting for the write-up?
I get it, it's hard. I have one employee who ALWAYS argues with me. i can ask him to do the simplest thing, and he turns it into a discussion. I finally got tired of justifying what I was asking of him and said that I was done arguing with him, it wasn't up for discussion, and please do it.
He totally backed down once he was called out on it.
Hopefully, you can address sooner rather than later so that D chills the fuck out and acts like a professional.