I [19M] spent New Year's Eve with my girlfriend's [19F] family. My mother [46F] didn't like it, said some things to my girlfriend and now she wants to break up

Hey, reddit, I really hope you guys can help me with this one. A little background story first, I'll try to not make it too boring:

I've been with my girlfriend (who I'll refer to as "L" from now on) for a little over 2 years now. She is the first girl I've ever dated (in fact, the only girl I've ever kissed), I deeply love her and I know she does too. Even though we are both very young, we built a strong relationship which made us extremely happy.

Well, of course our relationship was never perfect. We had some arguments and she has already mentioned once or twice that she didn't like the way things were going and even mentioned breaking up before. Also, her father is almost overprotective and at the beginning we were very restricted, but as he got to know me better, things changed a lot (he would always compliment me saying I study hard and have nice career plans and other stuff). Little by little, he started letting us go out together more and I would visit L in her house three times a week or so (we live very close to each other). There was a problem though, he would almost never let her come to my house and it made my mother (who is always caring and receptive with everyone who comes here) feel bad.

(End of background story)

Flash forward to December 2016. I never spent New Year's Eve without my parents, which is nice of course, but I really wanted to spend it with L for the first time. Basically, my parents would go to a beach house with their long time friends and L would go to her grandmother's house in a city very close to ours, where they would have a family party and all of that. L invited me to go with them and I was over the moon, although telling that to my parents would not be easy.

So I went and asked them about it, my father really liked the idea and offered his support right away. My mother though was not happy, but I am an adult after all, so she respected my decision.

Well, I thought everything was OK and as the 1st of January came, I called my mother, wished her a happy new year and she did too and asked to speak with L. Of course, I passed the phone to her, a huge mistake which I'll never forget. Right after, L looked sad and didn't really wanted to talk to me all that much. I couldn't imagine my mother saying anything bad to her as they always got very well together and even texted each other once in a while. Only after some effort, I was finally able to understand what had happened. As L told me, my mother said something like "look L, I really want to gain a daughter, but I don't want to lose a son" (which was supposed to have an effect of "I really like you, but I miss being with my son", I guess).

That devastated L, she has great respect for my mother and was sad to make her feel that way. We came back from our trip on the 2nd and on the 3rd she texted me saying she really wanted us to break up. She was nice and tried everything not to make me feel bad. She said we had a wonderful relationship, but all the things around it were causing problems we could not solve or ignore anymore. She didn't say anything about my mom, or her dad, or any other specific thing like university, our intimacy and so on. Also, I have absolutely no reason to suspect there is another guy involved, at all.

Well, sorry for the long post, but all I want to say is that I really love that girl, I do not want any other girl and I don't feel the need to look for others. I don't care how many fish are there in the ocean, I never did. I am trying everything but I am not able to change her mind. Also, how would I say all of that to my mother without hurting her feelings? I know she didn't intend to say those mean things, I really do. Should I move on and focus only on getting my degree now?

tl;dr: Spent New Year's Eve with my girlfriend's family, and on the 1st of January my mother told my girlfriend she did not want to lose her son. My girlfriend, who I love so much, was devastated and ended up breaking up with me.

Ps: As you may have noticed, I am not a native English speaker nor do I live in an English-speaking country, so please forgive any mistake and understand that translation is not always 100% correct (talking about my mom's quote, but it was the best way I found to say it). If there is any part you want me to clarify, I will happily do so. Thank you so much, any help is greatly appreciated.