I'm sure this topic must have been covered off before so I'm happy to be pointed to any articles etc that I may have missed while searching.
I need to implement a very simple REST API to add and retrieve records in a master/detail relationship. My two options are below:
GET /master_and_details/[master id]
REST more or less dictates option 1, option 2 is just a plain old http api.
Your statement that a master makes no sense without at least one detail is probably wrong. You have no idea how your api will be used in the future by clever developers. You can guess, but you don't really know.
If you really need the compound solution yourself you could always add an interface at a higher level that calls onto the two separate interfaces and returns a compound object.
Option 1 allows the possibility of a microservice implementation -- or at least, a separation of concerns into two separable objects. Option 2 alone would not.