So why exactly is "the shirt is under the trousers" a wrong answer?! I am not speaking American! Usually Duolingo is better at understanding that there are two forms of English.
Sometimes viable alternative translations are not in the database simply because no one has thought of adding them yet. Consider that Duolingo is America-based, so the first translations to be added generally use American English. I can't see anything wrong with your translation, so I'm sure it will be accepted if you report it.
Hose is feminine (die Hose).
Only masculine der can become den, in accusative only.
In this sentence you need dative, not accusative, so die will become der.
With unter and if there's movement from one place to another, then you would need to use the accusative case. But even then die would stay die, not den.