If I wanted to change the statement to distinguish between some people and a woman, could I say:
For her: Die Miete der Frau ist hoch.
For their: Die Miete dieser Leute ist hoch. [or] Die Miete der Leute ist hoch.
Yes, that would be perfect. Though, to be honest, I can't really imagine a situation where this would be necessary as context should clear up any ambiguity.