Heya Sagey.
I find that the most magical thing with language, is that many words you can divide. Respect in it self have a definition. So the word will never mean something that is different from the definition. However, if you deicde to add something. Like "Respect towards my idol" or "respect towards my fellow human being" Then you add some to the word.
Behalf on your mother, I can not say if she is right. When it comes to you being rude. I have not experienced your situation. However, for what you write here. You do not seek them out, but you answer if you must. That to me does not sound rude (of course it depends on the tone, which I do not know how it is. Since I am not there. So I neither claiming that you use a proper tone or not). I myself in the age of 17 to 20 Experienced this. If it is similar I am not sure of. However, I started hating does people a lot. I was however, more rude then you. Since I did not answer them, or only did in aggressively. Nonetheless, when time passed and I got to learn myself more. I started to remove the hate towards them. I even once helped one of them, when the person dropped something. I helped that person by picking it up.
After I have "evolved" my personality. I answered them respectfully and polite. However, first time each of them approcahed me. Most of them would say that I have changed into something amazing (Which is of course discussable). However, for does who did tell me that, or something in the line. I first of thanked them for the compliment. Then I told them how diffucult they made the change, and I do not hate them anymore. I acctually have some sort of sympathy for them. Duo to the fact, that they had a need to discuss or come up with rumors about me and my friends. Which kept me from getting a job in the small town I lived in back then. What I found out to be my gold mine. Was to find out who I was, what made me happy. I remember the first day I asked myself that question. "who am I", I spend 3 hours just sitting in a room thinking. Overtime I got to learn myself. I can before hand tell you what will irritate me, and I do not do as anyone else does. I even left my old friend group, cause they where just not me. Know I have a lot fewer friends but they are more friends then my older one was.
What I am trying to suggest. Cause I do not know the answer, I only know what is right for me. All I can ever do to offer you anything. Is by sharing my experience, and then just hope that you can use it to something. So if you do not know, like really really do not know. Find out who you are. It made me so much stronger, these day I do not care what people say about me. Cause I know what makes me happy.
Next time you are in the car with your mother. Try to speak with her agian. I got all 4 of my raised sallary by talking with my boss when I was out driving.
Sorry for this long comment. I just felt like sharing it with you. You seem to be doing alright at the moment. I hope you find a solution to the problem, and learn how to move pass it.
Best of wishes and hope you have a good day/evning.
Cheers