I see two entirely plausible stories that happened here. One is this tale the way LW framed it. And the other is, well, this:

• "My mother was holding him, obviously enjoying his exhausted cuddliness, and he was pale, relieved to see me, and a complete shell of himself.": I got home and overreacted to my child that I expected to be in bed sleepily cuddling with his grandmother.
• "I whisked him upstairs to bed": I icily grabbed him from my mother, saying something cutting I believed was polite.
• "In the meantime, while I focused on the task at hand": I ignored my mother, snapping that I had to put my son to bed according to his clear schedule, mother.
• "my mother decided I was violently angry with her, started yelling at me about how she had tried to put him to sleep but “he didn’t want to go,” and then stormed out of my house to drive home with my dad.": My mother tried to have a conversation with me because I was clearly angry, I ignored her, so she decided it was fruitless to stay and went home.
• "I said I was sorry I hadn’t given her more detailed instructions, and I would plan better next time.": I texted to her, "dear mom, I am could not attend to you as you left because I had to restore poor Alfred's still-disordered schedule, but I realize I couldn't expect you to be able to remember his very important schedule, so next time you come I will plan around your incompetence and not let you care for him at naptime."

Honestly I'd find either version equally likely from this letter.