My parent was traumatized by an experience they had as a young person, and their suffering affects our quality of life. How can I help them become less personally hindered, less fearful for me, and improve both of our lives?

It depends on how trapped they are. Are they able to hear you? Does your voice reach them? Find out what reaches them. Find out in what environment they feel relatively safer and what triggers terrify them. Try to create an environment where they feel safe and stabilize it. Wait for them to open up. Exercise infinite kindness and patience. Listen to them even if they are not able to coherently express themselves. Keep reminding them that the threat has passed and they are safe. Create safe space around them that can allow them to heal. Tell them that it was not their fault what happened. Tell them this again and again, as many times they need to hear it. If your voice does not reach them, seek professional help. If they are open to read and books help them: there is a brilliant book on the effect of traumas and what it does to a person (both childhood abuse trauma or due to experience as a veteran). Its called "The body keeps the score". It helped me immensely to understand what I was into and that there was hope for me to recover.