My general manager acts, speaks, and manages in a way similar to my abusive parent. This frequently triggers PTSD flashbacks.
What are my options to get her to stop? Solutions I've thought of are potentially involving HR, or just quitting this job.
Please get help from a mental health professional. Follow their advice over anything you may read on the internet.
That said, I'm afraid you cannot do much here other than escape the situation. Even if (and that is a huge "if") everybody involved, the general manager, HR and everybody else genuinely wants to help you, there just is no way. The way someone "acts, speaks, and manages" is deeply ingrained. While changing management style might be an option, changing acting and speaking patterns is serious work. Especially when that person has no idea which patterns exactly trigger your PTSD. So in other words, you could talk to the general manager directly, or even to HR, but what actions could they possibly take? There is no realistic path to a solution.
If you really like that company, you could ask for a transfer to another team, assuming meeting said general manager in an elevator or canteen once in a while is acceptable. Otherwise, you'll need to find another job. A workplace that is harming you (even unintentionally) is not worth working at.
Solutions I've thought of are potentially involving HR, or just quitting this job.
Please don't do that. Especially quitting the job. Your situation is understandable. You are facing an uncomfortable situation and quitting your job may make matters worse. Unless you have an offer in hand which aligns with your career progression goals.
It won't be a good approach to talk to HR as the first step. Assume you talk to the HR. They will probably involve your manager in the resolution talks (either by talking separately or together with you). This can make things bitter between your manager and you, and make it tougher to resolve the issue by setting a wrong tone.
It's never good to give an impression that you go behind someone's back to resolve an issue instead of talking directly to the person concerned.
What are my options to get her to stop?
The first approach would be to talk to your manager. You can send her a semi-formal request seeking some of her valuable time to speak in person about a crucial matter which is affecting your work. Keep it simple. Keep the tone such that it is non-offending.
I would like to seek your guidance in a matter which is affecting my day to day productivity.
Kindly consider giving me a suitable time slot (of 15-30 minutes duration, per your preference) where I can speak with you in person. I could really use your insights in resolving this issue.
I think that should do. Once you get a chance to speak to her in person, set the tone in a way that you are seeking her assistance and how her inputs would be helpful. Revealing only as much details as you are comfortable, tell her about your PTSD issue and how it affects you work performance. Your tone should give a slight hint as to how similar occurrences from her end (although unintentional) may be affecting your productivity.
If it makes you feel comfortable, and is feasible, you can also request her to meet in a public/non-office place.
I think gaining your manager's trust and seeking her assistance in resolving the issue could be the best approach to take. It sets the tone right.
If you feel that talking to the manager hasn't improved the matters to make the work situation comfortable for you, seek assistance of HR and ask for workplace counselling. Please don't set the tone that the manager is causing the issue, no name calling. Instead, seek assistance by telling that some work life issues are causing a dip in your productivity and you could use a general counselling that can help with improving your productivity.
Decently sized organizations do adhere to such requests, and take such employee mental health related counselling seriously.
I think the above two would certain help with making things comfortable for you. A good general approach to take is to focus on identifying the issue and how it could be resolved best in an amicable way rather than laying blame on the people involved.