There is really good advice in that video; do watch it.
I think my kids are old enough to handle it if something unexpected happens, but it's got to be really tough when the child is younger and more unpredictable. I think you have to walk through all the possible security procedures so she knows what to expect, and explain that these procedures are part of flying, and that you as a mom don't have control over which ones are or are not selected on any trip. Then keep a close eye on her as you go through security, and watch for any tell tale signs. Pull both of you to the side of the line and talk to her if you see signs of stress. If you are proactive, you might be able to find an employee willing to help you and your daughter through.
Find and select less popular times to travel, so the agents are less likely to be stressed, and more likely to slow down and try a better approach. Check what procedures different airports use, and decide which ones are the most acceptable for your daughter.
Obviously allow lots of extra time for getting through, in case something goes wrong.
Boarding passes can usually be printed from home, btw. Do it. One less thing to go wrong.
Most of us aren't willing to risk not getting on the plane to make a protest, so that leaves you in take it or leave it position.
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Mom to an amazing young adult AS son, plus an also amazing non-AS daughter. Most likely part of the "Broader Autism Phenotype" (some traits).