literal Eng-Pol translation is "Ta Pani nie jest w domu", grammatically correct sentence that is rarely used. (It means more "the place where she is is not home")
Literal Pols-Eng translation is "it does not have this lady at home", which does not make sence.
It is a phrase "Nie ma"+ a person/thing "missing" in genitive+ location
You were close, if it was Nominative (Ta pani) this would indeed be "This lady does not have a home".
I'd say "There is not (or even 'There has not') this lady in the house" to be the most literal translation.
The lady here is in Genitive. If it was a less surprising sentence about lack of... vegatables, or a computer, in the house - that would still be Genitive.
Sounds strange. It is correct sentence, but this word order is uncommon. Usually the sentence "w domu nie ma" is about something missing/lacking in the house/home like salt, tomatoes, heating, love. so in order for this sentence to have sense "this lady" has to be a specific member of your houshold, your stepmom probably.
This was a great post for me. I can now wrap my head around the translation and now sentence makes sense to me. I realize that the word order does not work so that I need to say it the way it is written in answer at top. However, this post allowed me to "get it". Thank you!!!