Sounds like an unhealthy situation for everyone involved to me. Grandparents threatening to pour bleach into you tank. You threatening harm to their cat in retaliation. Pets caught in the middle of the feud on both sides. Me thinks the best thing to do is either live by their rules, it is their house after all (rent or no rent), or go get your own place where you make your own rules.
Barring that, you could most likely power the tank heater with a car battery & power inverter. But that's a lot of trouble.
Barring that, you could most likely power the tank heater with a car battery & power inverter. But that's a lot of trouble.