Landlord is theoretically under no obligation to pro-rate rent, but that said, if you leave in ten days you save your rental history (an eviction shows on your history the day it is filed, not later when a court makes a decision), and you can certainly decide whether to sue her to recover the rent you paid but did not get to use because you had to leave or be evicted. Depending on the facts, a court could agree with you.
When your landlord is unreasonable, the smartest thing you can do is to cease rewarding her unreasonable conduct by leaving. If you leave, she has to get new tenants or lose a substantial sum of money. You cannot effectively have a lawsuit while living in the same property as your landlord. If you had a lawyer you could well get this to trial, but by then the damage is done.
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