How to get my mom to yes to getting me a puppy?

Ohkay, I really want a puppy (shih-poo to be exact) and I am extremely responsible. I have taken care of my 3 year old brother for the last 3.5 months while she's on the ship, and my dad's in japan. (My brother and I were evacuated because of the natural disasters & radiation). So, I'm going back, and I really want this dog. I promised her I would do everything for the dog, and she wouldn't have to be even near it. ( She says she doesn't like dogs ) . But she still says NO and then she changes the subject. I'm really a good child, and I get good grades. Please SOMEBODY help me convince my mom to get me a puppy. Can you tell me things I should say to my mom to change her mind on the dog. I've done so much research for the dog, I even tried to get the cheapest one, but she still doesn't want it. My dad says yes, however, and my brother wouldn't care less. All my family members, - aunts & grandma - say that I would be suitable to get the dog. BUT SHE STILL SAYS NO. She's being very stubborn, can somebody PLEASE help me.