possessives - Correct Grammar Surrounding "Asylum Seeker Children"

I was wondering what the most appropriate wording would be for the following instance.

Today I will be illustrating the complexity of the issue that is
whether or not asylum seeker children should be retained in Australian
detention centres.

Should it be 'asylum seeker children', 'asylum seekers' children', or should I choose a different route altogether and merely go with, 'children of asylum seekers'?

I assumed it would be 'asylum seekers' children' but the wording on my essay handout says the former.

Answer

The matter of asylum seekers and their treatment is a current and sensitive topic. This answer comments only on the English construction of the phrases suggested, without commenting on the issue itself.

Your three terms refer to children, but not in exactly the same way.

As @HotLicks mentions, "children of asylum seekers" is the clearest of the terms you suggest, and asylum seekers' children carries the same meaning, that is, children whose parents are asylum seekers. Strictly-speaking, the term does not necessarily call those children asylum seekers.

In contrast, the term asylum seeker children has children as the head of the phrase, so the noun phrase asylum seeker modifies children. That is, the term refers to children who are asylum seekers. Strictly-speaking, it doesn't call the parents of those children asylum seekers.