Here is the explanation from the Cambridge Dictionary for HUNKER DOWN:
to sit down on your heels:
We 'hunkered down' around the campfire, toasting marshmallows.

Do you use 'hunker down' this way often? I've made some sentences below:
1. My son hunkered down in the shower, washing his hair.
2. I ask my son to hunker down before I wash his hair.
How do they sound?

Thank you very much. :)

Question

Here is the explanation from the Cambridge Dictionary for HUNKER DOWN:
to sit down on your heels:
We 'hunkered down' around the campfire, toasting marshmallows.

Do you use 'hunker down' this way often? I've made some sentences below:
1. My son hunkered down in the shower, washing his hair.
2. I ask my son to hunker down before I wash his hair.
How do they sound?

Thank you very much. :)

Answer

It means literally that but it means to settle in and prepare for something bad stressful to happen, which you are going to weather (e.g. a storm), or to close in around something and get close to it or other people around you (e.g. around a fire), especially if it evokes a feeling of solidarity or safety.

E.g. the kids hunkered down around the campfire and told stories to each other
 or, 
they hunkered down in their bunker, watching the news.

So the first one works if he's really intensely washing his hair, but the second one doesn't work because it's really not (usually) a stressful situation. If, unusually, it is going to be, then you can use hunker down there too.