I was wrong.
She saw it through the window of the back door before she even made it IN the house. I opened the door (her hands were full) and she was staring right at it. She dumped the things in her hands in the kitchen, and grabbed the video with her coat still on, and made for the bedroom and the rest of her videos. As she scooted off, I prompted her, "What do you say?" "Thank you!" Over the next two days, she'd appear in the living room, video in hand, and tell me thank you again, and again, and again. Marc suggested the video's absence had left a big, gaping hole in her life. I suspect he was being funny, but her reaction suggests that he wasn't far off the mark.
Once again, I have proven I am Übermom - capable of fixing any problem, righting any wrong, none are too small. Unfortunately, things like melting snow are a bit beyond me, so she will be quite angry when she gets home and tells me she wants more snow. And I don't produce any.
Rash update: Apparently it was the detergent. After rewashing everything in Tide Free and Downy Sensitive Skin, her welts are fading fast, and no new ones have appeared since she been wearing clothes not washed with the other stuff (Arm & Hammer w/ Oxy Clean).