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: 
> 
> What do her parents do?
> 
> 
> 

Here the subject of the sentence is *her parents*. Because *her parents* is plural the auxiliary verb *DO* must agree with the plural noun phrase, so we need *do* and not *does*. The auxiliary verb *DO* is the first verb in the sentence. This is the verb that moves in front of the subject. It has no meaning, it just helps to make the sentence a question.

The verb after auxiliary *Do* is ***ALWAYS*** an infinitive. It can never be "Xing", "Xs", "Xed" or "to X".:

* Does he ~~eats~~?
* Did they ~~went~~?
* We don't  ~~liking~~...
* They didn't  ~~to come~~.

It should be:

* Does he eat?
* Did they go?
* We don't like ...
* They didn't come.

We can only have one auxiliary verb *DO* in a sentence.

However, the second *DO* in the Original Poster's example is the main verb. It's the lexical verb *DO*. It isn't an auxiliary. Because it comes after the auxiliary *DO*, it must be in the infinitive. The verb after *auxiliary* *DO* is ***ALWAYS*** an infinitive. Therefore the sentence must be like this:

* What do her parents do?

Hope this is helpful!
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.