doesn’t this definition lack a recursive case to ensure that the mother is either Eve or a descendent of Eve

We don’t see the definition of mother. It might already encode that Y is a person.

And there should probably be a father case in there as well?

While every person does also have a father, it’s completely redundant, since being a person can fully be described by [Edit: ~~being~~ having] a mother (or being Adam or Eve).