How can I get my iPad to automatically connect to my iPhone's hotspot?
To get that feature, you need to "Set up Instant Hotspot" which is part of Apple's Continuity feature. 

https://support.apple.com/en-us/ht204681#hotspot


  Use Instant Hotspot with any Mac, iPhone, iPad, or iPod touch that
  meets the Continuity system requirements. It works when your
  devices are near each other and set up as follows:
  
  
  Your iPhone or iPad (Wi-Fi + Cellular) has an activated carrier plan    providing Personal Hotspot service.
  Each device is signed in to iCloud with the same Apple ID.
  Each device has Bluetooth turned on.
  Each device has Wi-Fi turned on.