Based on the games you are playing, I don't see why you wouldn't be able to get Grand Theft Auto 4.
But GTA 4 is very intense and graphic, there are times when you get to execute people, and when you get to choose peoples' fate, on whether they live or die.
I don't know if they made you want to play it more, or what, but theres just some information for you…

Maybe the fact that you can beat up cops

Its not very bad at all. Especially if your already playing M games.

It is said to be bad for children, but seeing the games you are playing, there should be no problem. Maybe she just thinks that you have too much games already and might not want to spend for more.

there is no rational thought for the parents besides just the name of the game, it got a bad parent rep and they don't know about the other games content. but I will say that it is pointless, random violence instead of having a decent story to it (ok GTA4 had a story but you can still do the random violence). I would tell you not to get it though, looking at your list you have pretty good taste in games (besides WAW, COD4 rocks WAW anyday) but anyway…gta 4…. the controls are sloppyesk (like army of 2 third person view) and the car controls are absolutely dreadful, I found myself bored of it after 3 hours because there was nothing to do besides drive people around and even with the gun cheats and helicoptor cheats it was still lame because there are tons of invisible walls (into buildings and other vehicles like airplanes) which sucked. I you should ask for a game that is better like left 4 dead or fable 2 (if your into that) and seeing as you don't have mass effect, GET IT USED it is awsome and you would love it, i promise, same with metal gear solid 4 guns of the patriots

Perhaps its the realism. It looks like everything is possible. (except for your magical cell phone) In fact the entire game is fairly possible. Maybe your parent(s) think you'll want to imitate this, which you surely won't.