When I attempted to translate this sentence into German:
She said, "I wouldn't want a strange man in my house to teach me."
I said:
Sie sagte, »Ich würde keinen fremden Mann zuhause wollen, um mich zu unterrichten.«
and was corrected with:
Sie sagte, »Ich würde keinen fremden Mann zuhause haben wollen, um mich zu unterrichten.«
How does the meaning in English indicate the necessity for "haben" and why is it incorrect without "haben"?
The difference lies in the verb "zuhause" describes. If used without "haben", "zuhause" describes "wollen". In other words, you want him while you're at home. This is probably not what you meant, although I think that this is also a valid interpretation of the English sentence.
If you add "haben", "zuhause" describes "haben", leading to the intended meaning that it's the man who is at your home.
But I think both sentences sound awkward, because the "um mich zu unterrichten" clause also seems to modify "wollen". If you want to keep that sentence structure, I would say:
Ich würde keinen fremden Mann, um mich zu unterrichten, zuhause haben wollen.
Generally, it is better to translate with "wollen, dass":
Ich würde nicht wollen, dass ein fremder Mann mich zuhause unterrichtet.
