Dude, she's trying to help you. Trust me, I'm 17, so around your age, and almost off to college. My whole life my parents have stressed to save my money, and their whole life they've saved their money. I've always listened to them because of how well it turned out for them. I'm assuming you want to go to college, and unless you are lucky enough to have your parents pay for that you're gonna have to pay for it yourself, and that's a huge financial burden, and every penny counts.
I'd trust your mom's judgement, it sounds like your sister is older, and your mom probably feels like she can't have your sister live under her rules anymore, but she is only trying to help you. Trust me, I'm starting to realize that saving your money is a lot more important once you get into the college time.
If you want Red Dead Redemption try selling MW2, and maybe one other game and then use that to go and buy it. I'm sure your mom wouldn't have a problem with that since you are taking initiative and finding a way to get something you want by sacrificing something else.