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Actually, if the street were narrow and I wanted to omit "on the other side" part I would myself say
"Моя машина стоит перед твоим домом."

I would say
"Моя машина стоит напротив твоего дома на другой стороне улицы."
But I can easily imagine somebody saying "перед твоим домом", especially if the street is not wide.