lol, i never EVER asked my parents for a pet when i was a kid, i snuck it into the house, and my dad who is very intimidating according to everyone has a very soft spot for animals, especially the cute and cuddly, so even if a slight argument broke out about the pet, it was resolved quickly enough when i was like "look dad, just pet it, aw it likes you, look at it wash its face.." you'd see him try not to look but it was inevitable, he always fell in love to... mom on the other hand never presented a problem, usually just saying "hide it from your father for a while" gotta love em eh? lol...
if i were you i would print up some info about rats and have your mom read it, she may be thinking that you telling her that rats are happier in pairs or more to be your way of acquiring more rats than you can handle, i'm sure that after reading that they ACTUALLY are happier in pairs she'll cave in.