It sounds like your mum is just frustrated because she wants whats best for you. She has made sacrifices for you (not living in her birth country, the expense of private education) and she expects you to make them for her by putting in the work and going to Cambridge as it may benefit you in the long run. But Cambridge isn't for everyone. This is an attitude that she has to change and not you. It's your life and you must live it the way you want to, or you will be unhappy forever too.
Also, I wouldn't worry too much about AS grades, if you put in the work next year you will still do well. There are so many people with high A-level grades that Cambridge look at much, much more than your grades so you will have plenty of opportunities to impress them.