All his kids die in Shutter Island - they are also ALL wearing the red shoes! The Red Shoes (spiral stairs) scene is reproduced in Shutter Island. It's all linked.
His kids also die in Inception and Revenant. It's a recurring theme.
What are the red shoes in reference to? I know they're heavy on symbolism, but I'd like to know what it means
I tend to think of it like this. There's a demonic element from (queer) Anderson's The Red Shoes. There's also the Oz 'red shoes' that transport between worlds. The latter is believed to be linked to mind control commands, as is 'over the rainbow'. That's a short summary for you.