I ride, and like you, have come to the conclusion that everyone using their left turn signal is trying to kill me.
Given the choice, your family would prefer that you are scary and alive rather than invisible and dead.
I hope she feels equally "like shit" that she frightened you.
story time.
Many years ago I was stopped at a sign waiting for a break in freeway traffic (no onramp, just a stop sign for traffic entering a four lane highway). I looked in my rear-view because I wanted to see if it was prudent to wait for a friend approaching on the highway. All I could see in my mirror was rapidly approaching "YO". I dumped the clutch and released the brakes in an effort to get out of the way, but the toyota pickup hit and threw me onto the highway.
I picked myself up, verified that I was intact and wasn't in immediate peril of getting run over by the highway traffic, removed my helmet and turned to look at the car that hit me. The bumper was caved in, the grill was destroyed. the hood was v-notched and buckled about 8". A young woman got out of the truck, said "Oh shit, my mom is going to kill me."
I said "your mom is the least of your problems".
I'm a pretty benign guy, but in those days I spent quite a bit of time in the gym, I lifted a fair amount of weight, and I was wearing a tank-top and a nontrivial amount of road rash.
She looked at me for about 2 seconds, then silently returned to the truck and locked the doors.
The cop gave her a ticket for "failure to yield" which I considered a fairly light consequence of the dumbfuckery inherent in rear-ending a motorcycle at a stop sign.
I rode the bike home but the truck had to be towed. I hope she learned a lesson about sharing the road, as I learned a lesson about protective riding gear.
/story
I guess I didn't answer your question. I will say this; I think your anger served you appropriately, and that you exerted the right amount of control over it.