Lost...

21M (me) got involved with 24F (Alice) over the summer. Our families are very intertwined, me being Alice's brother's best friend (Bob) for my entire life, our mothers being best friends as well. Things started off seemingly spontaneously; both sides developed an attraction at around the same time, which is odd considering we have known each other our entire lives. We told Bob, my brother, and Alice's mother in September. Bob and my brother did not care, but Alice's mother disapproved because of a few reasons which I'll discuss below. As a result of this, we legitimately tried cooling ourselves down and being friends a few times, only to completely cross that out when we met in person, every single time. (LDR, I go to school, come back every 2-3 weeks. She lives with her mom and Bob).

Fast forward to November, things have been going great for a while, but my mother still doesn't know. I decide to tell her towards the end of the month, and she is shocked. Not because she thinks Alice is a bad person, but because we have known each other our entire lives, a sentiment that Alice's mother also shared. My mother tells me she won't get involved, and to "be careful." I tell her that Alice and I both don't want to get our families involved, knowing how intertwined we are, and that we want whatever happens between Alice and I to stay between Alice and I, only. Also during this time period, Alice and Bob slept over one evening at my place (I also stay with my mother), but this was before my mother knew about Alice and my interactions.

One week later, I'm back at school and I receive a phone call from Alice. Apparently, my mother has upset Alice's mother by saying a few things like "why wouldn't you tell me if you knew, why would you let your daughter sleep over if you knew," etc.. Alice decides to break things off with me, under our agreement that if people other than us decide to get involved and get hurt, then we have to stop being selfish and think about others and end things. I am upset by this, and after a few hours of deliberation, I confront my mother and ask her why this has happened, and ask that she apologize from them both for hurting them, and hurting me. Instead, she decides to make things worse and confronts Alice's mother about this, which hurts her even more. Later that evening, I receive a phone call from Alice, and she says that she can no longer speak with me as per her mother's wishes, and that her mother will be monitoring her e-mail, facebook, phone, etc. to make sure that we are not speaking. Additionally, her mother has cut off all contact with my mother, and me as well.

Fast forward to a few weeks later, and I visit Bob at their place. Their mother does not even acknowledge my existance, and though I greet Alice enthusiastically, since I have not heard from, or seen her in nearly a month, I receive a quiet "hey" back, so as to hide that we even interacted from her mother, who is in the next room. She then proceeds to walk past me with a sour look on her face.

I'm having trouble coping with this. For something that was going on for only about five months, we both formed a deep attachment and emotionally and physically, things were extremely powerful, almost every single time. One evening when we came to my place, we noticed that the stars were shining really bright, since the sky was so clear. We went stargazing that evening, and every time it's a clear night, my heart sinks knowing that that won't be anymore. I try to distract myself doing things, but always seem to have her in the back of my mind, because neither of us wanted things to end this way. I have dreamed about her almost every evening in my sleep for a month now. I don't know what to do.

TL;DR: Fell for sister of best friend of 20+ years, families got involved, can't speak with her anymore.

Edit: Some more details:

A few other issues concerning my mother and Alice's mothers objections to us include our age gap, and how she will likely be ready for marriage before I am, and how Alice's mother will likely press for that to happen if we date for a few years. Also, our mothers are part of the same community / friend circle, and don't want other people really knowing or getting involved in this.

I have spoken with my mother about this, she refuses to call Alice's mother and apologize for what she has said, because she believes she has done nothing wrong. She refuses to "beg for her forgiveness," even though I have explained that obviously there was some sort of misunderstanding and that no one is in the wrong here.

Edit2:

Thanks for the replies everyone. I do really appreciate the time you have put in to read about my situation and come up with a response. I have read and re-read all of them, and it seems like the overwhelming consensus is to speak with Alice about this. I think that I will likely attempt this in the next few days, when I have a better idea of what exactly I need to say.