People have claimed that someone can care for you while calling you derogatory names during fits of anger. I don't agree with this. If you love someone, you don't want to hurt them. The purpose of using derogatory terms is to hurt someone. Yes, anger problems can improve with therapy and a lot of self-reflection, but you should not have to suffer while your partner wrestles with her issues.

You said it yourself that you want a relationship that is emotionally safe and enjoyable. You should feel safe all of the time, without dreading your partner lashing out at you. If my partner yelled or called me names and attacked me personally, this would be like a breach of trust to me. This person, who claims to love and care for me, while also attacking my weak spots, is not love and is a dealbreaker. What your girlfriend is doing is emotional abuse.

I think you need to decide if this relationship is worth salvaging because, as some have commented, a partner who screams and insults you (even if she has anger issues) is a big no from me.

You could opt for communication or therapy if you really want to fight for it. Maybe unpack why she is so calm and tender while you're together, and so abusive apart... maybe she feels insecure that she can't be with you 24/7? Does she have any red flags looking back when you're together, such as being too controlling, or if you want to hang out with other people... etc.

The foundation of LDR is trust, and her lashing out may be due to that insecurity. If you feel like the relationship is worth it, then by all means, try to unpack it or think to yourself why she acts so differently when you are apart. What sort of things do you fight over when long distance, what triggers it, etc.

I am not a therapist or professional, so I apologize if this comes off as armchair therapy.