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: 
To answer your specific question, *Can you have **does** and **do** in the same sentence like the first one?*, Yes, you can. You can have *do* twice, but not *does* twice. This is not a very helpful rule, however. The role that each word plays is very different in each case.

The first use of *do*/*does* is just a way to construct a question in English. It has nothing to do with the second use, which is what the question is really about. Try with a different verb in the question:

*What **do**/**does** her parents **cook**?*

Clearly, the word *cook* is irrelevant to whether we should use *do* or *does*. In reply to your hypothetical question, you could preserve the *do* to give a more assertive tone. 

*Her parents **do** cook.*

*Her parents **do** do.*

Or in singular form:

*Her father **does** cook.*

*Her father **does** do.*

So there's nothing wrong with a sentence with multiple uses of *do*.
The correct question is, "What do her parents do?"
Since the word 'parents' is plural you would use 'do.' 
Of course if you had the word 'parent' instead of 'parents'you would use does.
"What do her parents do?"
"What does her parent do?"