I have a VERY LOOOONG story and learned a valuable lesson from my ex that I dated from when I was 16 to 20. But I'll keep it short trying to get my point across.
1) There's a reason why you guys aren't dating anymore. Is it a logical one that leaves you both better off? Obviously not. Her reasoning to break up with you sounds very immature. Just because you were grounded doesn't mean she had to break up with you and find someone else (which gives a good example of her character. She needs someone for HERSELF, not in the interest of you or her current bf). I'd be extremely upset if my girlfriend cared so little about our relationship that she just ended it instead of fighting through it to be with you, but instead needed someone available/convenient so she dropped you to find someone else.
2) This girl is seeing other guys. You make it sound like she's been in SEVERAL relationships since you guys broke up. Im CERTAIN you're not the only one who feels this way about her right now and she's laughing about it with her friends. I know these girls TOO well. They feed off the pain of their boyfriends and cover it up with a sincere "I'm still a good person, and you're the problem" to the point of making you sound like a borderline-abusive dick no matter what happened. In your case, probably "ignoring" her because you were grounded. You'll lose braincells trying to reason with that, so don't try.
3) There is a reason your heart wants her back and your brain doesn't. It's because your heart is stupid and that's WHY you use your brain to do what makes sense. If you loved something that caused you pain, would it be logical to keep doing it? Hell no. Like, look at all the smart people on heroin! Oh, nvm, they're dead.
4) If you're crazy enough to try and want a girl who only wants you to be around to keep her company, well I suppose you could fight her current boyfriend. This happened when my ex threatened to leave me for my best friend (who also liked her) and I told her to GTFO of my house and life (too her surprise, she didn't know how tired I was of her crap). She reluctantly went on to date my friend (who, as a result, was shunned from our group of mutual friends) before I knocked his teeth out in the dirt for disrespecting/betraying me as a BROTHER, not even a friend. It's very sad to see people get hurt over a girl, it's even more F'ed because that's what they want. It makes them feel above others.
5) It's not "wrong" to get between people if you share mutual feelings, but prepare to fight for what you want and know what it means losing (in my case, it was a friend). In your case it's just not logical/worth it given the facts.
I'd wait until you're both older and more mature about these sort of things. Give it a couple years and some space. I can tell it's too early for you to make any logical decisions. If you guys dated for a while like I did, these feelings may never go away. Mine didn't, they were recycled into a seething rage that was released when my ex's bf tried talking to me about her. My love was replaced with bitter hatred peppered with disgust for her way of thinking that I wasn't good enough for her. Don't turn into me.
Good luck man