How can I convince my mother that I am ready to adopt this rescued kitten? URGENT!?

Make sure she knows you'll take care of it 100% so she never has to even think twice about it. Pay all vet bills (but be prepared, they can get big!), and tell her it'll wind up in a shelter to be killed or be let outside to fend for itself. You can make it seem like something terrible will happen to it ;). Just tell her how much work you're willing to do with it and even tell her that if she's not happy with how you're taking care of it, THEN you'll find a new place for it to live. I guarantee she won't make you get rid of it when it's in the house, but I'm sure she'll find solace in knowing she has options. And make a point that if the dog hasn't attacked before, I doubt he'd start now. That's a silly reason.