Why do my alternate icons work on iPhone but not on iPad?

You have to add images for the ipad resolutions too. And they're name must be something like icon@2x~ipad.png. That ~ipad is the difference

The sizes for ipad are

iPad Pro        167px × 167px (83.5pt × 83.5pt @2x)
iPad, iPad mini 152px × 152px (76pt × 76pt @2x)

A separate CFBundleIcons entry in Info.plist is needed specifically for the iPad. It must be named CFBundleIcons~ipad. Just copy your current CFBundleIcons entry and rename it.