¿Qué hace tu padre?
¿Cuándo trabaja tu hermana?
I would think:
- ¿Por qué es vendedora tu madre?
is the appropriate word order but it turns out to be
- ¿Por qué es tu madre vendedora?
How to make sense of this? How to remember it?
Both options are correct. And others.
In Spanish, since the words are properly modified (the verb is conjugated, and the names and adjectives are coordinated), there is some elasticity to order them.
This is usually done for stylistic purposes, but can be done also for meaning reasons.
This one stresses the fact that she is a seller. Would roughly be "She is a seller. Why?"
This one stresses the fact that the asker talks about your mother. Would roughly be "Let's talk about your mother. Why is she a seller?"
This one follows the standard order of words in Spanish: subject "tu madre", verb "es", predicate "vendedora"; so it does not stress anything in particular. This one is the standard way of asking this question in most Spanish-speaking places. But note that there are regional differences.