I am sorry to hear how you're suffering.
The first thing I thought in reading your letter was that I really am not clear on why she broke the engagement. It sounds too vague.
Have you spoken with her at length? If not, I would do that right away. Tell her what you told me about how much you love her and can't forget her, then ask her to please explain in more detail what went wrong with her family. We don't know if they don't approve of her getting engaged so young. Or whether they have some issue with you.
For example, do your religions differ? Do you come from a different socioeconomic class? It sounds like she may be a very meek and dependent girl who is too afraid to defy her parents. I don't know if this type of deference to authority figures is customary in her culture (I don't know where you both are from) or whether her submission is an indication of an emotional or developmental block on her part (this would be the case if she's an American girl who allows her parents to rule her).
Also make sure that she isn't using her family as an excuse. For example, does she not love you and is she using her family opposition as a way of avoiding telling you directly that she doesn't want to marry you? She obviously loved you enough to accept your proposal, so we want to know what happened within her or within the relationship to change her mind so drastically (if the break-up is truly due to her not her family).
When you have more facts, you will be in a better position to take action. If the problem is her family, then it would be good to talk to her parents and try to win their hearts. To do this you would want to tell them about how devoted you are to their daughter and, of course, listen and understand their objections.
Please don't give up on her without a bigger fight. If you have tried everything and left no stone unturned, then, if God forbid, there is no chance for resolution, you will feel more able to accept the situation, grieve, and finally let her go, knowing that you gave it your all.
I think that the reason you can't let her go is because you still don't know why she ended it and, for this reason, you can't be sure that there is no possible hope.
So go out there and slay a dragon or two. If she loves you, then your devotion will make her love you all the more. If her parents have reservations, your dedication should sway them to your side. Please let me know what happens.