What you should do is gradually introduce them. Cats are creatures of habit and don't like change. You need to isolate the kitty (not in the basement!! ) and then bring her out IN A CARRIER (for your protection and hers) and let the dog sniff her. ALWAYS make sure the dog is on a lead so you have control over him.

Brody's mom is right, she wasn't scratching your sister, she was trying to get away from the dog. I hope your mom will reconsider. The basement is a cold, damp place to spend the rest of it's life. If your mom insists that the kitty stay in the basement, maybe it's better to find a better home for her, one where she'll be part of someone's life, not just a fixture in a cellar.