Oh wow! Is there anything people won't try to feed goldfish to?
Good of you to take him in. If you want a good emergency home for him get a large rubbermaid container. I've seen ones as large as 55 gallons at Walmart. That's going to be much better than putting him in a 20 gal tropical tank. In warmer water goldfish grow faster. He'll produce more ammonia there and need more water changes. I don't think your mother would be willing to do 2-3 water changes on her tank per week.
Since it is the end of summer, you won't be able to plop him in a pond until next spring. You can't take a fish that has been living at room temps and expect it to survive in a pond in the winter. Plan to keep him over the winter.
While he's in that tiny container don't feed him. Any food in means more ammonia. Keep it in a cool, dark place. This will prevent him from darting into the sides and injuring himself more.