Question: > 
> * What does her parents do?
> * What do her parents do?
> 
> 
> 

Which one is correct? Can you have *does* and *do* in the same sentence like the first one? Would it be incorrect because parents is plural so *do* must be used throughout?

Answer: 
It's "do".

Think about the answer to the questions. "Her parents *does*" is incorrect, whereas 

> 
> Her parents do a mean chicken casserole.
> 
> 
> 

Is natural sounding and correct.
I saw you're struggling between "parent" and parents.

Let's start from your question. First, we need to see the subject here which is "parents", mean both of our mother and father, which means that this is a plural subject. For plural subject, you must use the root word. So,....

What does her parents do? (Wrong)

What do her parents do? (Right)

I saw that you ask Ste about the word "parent". The word "parent" here means one of the parent(father or mother), which is a singular subject. For singular subject, we must add -s, -es, -ies and more. So,.....

What do her parent do? (Wrong)

What does her parent do? (Right)

In conclusion, we must pay attention on the subject to see which is suitable for the sentence.