"Is there a maid at your house?"
You wrote it in Katakana (which is used for foreign words like "maid" which do not exist in Japanese), which is why it wasn't accepted.
オタク means: geek, nerd, enthusiast, otaku.
お宅（おたく）means: your house; your home; your family, and it is a formal way of saying so.
I don't know if お宅 is accepted but your sentence wasn't because you used オタク.
Katakana and Hiragana don't like that so teaching it that way would be wrong. Hiragana is used for Japanese words and Katakana is used for Foreign words. This is why you are taught ジョン as so and not in hiragana. You cannot use them interchangeably. Japanese has no equivalent to capital and lower case letters. Katakana and Hiragana are different alphabets used for different things. It doesn't treat is similar because it is not similar at all.
It is customary to use Kana as you said nowadays, but it is not always. There are cases where you can use katakana.
For Furigana (ruby text), we can use Hiragana or Katakana.
For stressing certain words we can use katakana.
If you study the literatures in the Meiji period in Japan, all the texts were written in Katakana. Hiragana and Katakana are originally two systems to denote the pronunciation of a sentence.
In this case if we want to stress お宅, we can use katakana. But it is not a common thing, so I did not report it.
Back then there were no "writing" exercise, オタク appeared in the "arrange the blocks" exercise so I tried just for fun.
But seriously, in real life, do not say あなたの家 to people who is not your friend. お宅 is preferred because it is more polite. p.s. お家 is not a common word.