I hope all goes well Tetra. My feelings are that your parents need support too otherwise this cycle is likely to continue. I wonder if they would be willing to go to Al-Anon where they could begin to learn how to look after themselves and their own anxieties. At the moment they are just projecting them into you.
Family dynamics are hard to change until one or both of you are willing to step away from what is familiar and learn to let go a little. At the moment you write more about them than you do anything else. Really...they seem a bigger issue than your alcoholism to you.
I hope your therapist can begin to work with you all on this.
My thoughts are with you today x