How do I live after I (unintentionally) triggered someone else's trauma? My apology wasn't accepted, but how can I at least prevent the triggering from happening again and/or making her feel worse?

If this is a question regarding guilt, I think you need to understand that it wasn't intentional and you can't beat yourself up for it, and you had done the most you could in trying to apologize. You will not always be in control of how someone reacts to the words you say, being conscientious and empathetic is the best you can do. And practically if you can try stay away from topics that may trigger her or use your discretion, again that's really all you can do, that and being a supportive friend like I'm sure you are considering you have taken the time to reflect on how your words have affected the people around you. Thank you for trying your very best, because that's all you can ask for!

Although it is our responsibility to be sensitive to the fact that other people have triggers, we cannot always know what those triggers are or how we might accidentally set them off. It's already kind of you to be considerate of others' triggers! So don't be too hard on yourself. Unfortunately, providing an apology doesn't mean it will always be accepted. I think you might just have to give the individual time and space to recover. At that point, they may be in a healthier place to consider forgiveness. Even if they aren't in a place to forgive, you can let them know that you appreciate them telling you that you triggered them because you've learned from it and will become a more sensitive/aware person. Even when we unintentionally cause pain, we can take steps to intentionally avoid causing pain in the future.

Sorry for your hurt. You didn't try to trigger the trauma. The first thing is to remember that it was unintentional. If you sincerely apologized and it was not accepted, that's the least you could do. Forgive yourself and move on, this is the next step with or without the person that won't forgive you. When you learn the triggers of a person, be careful not to press to hurt them. Time may make the person forgive you once the hurt is better. Once you care for another person, you will be careful with the words so as not to trigger anyone's trauma. God Bless!