My niece lives in a mobile home and her refrigerator quit working after circuit breaker went off. She said it was because her mother in-law was using too many things at once so she wants her to pay for the refrigerator. Should this have caused the refrigerator damage if the wiring in house is the way it should be?

No, when the circuit breaker is reset the refirgerator will work just fine. The circuit breaker is just a switch and its tripping off is just like turning off the refrigerator or unpluging it.