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!
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.