I'd say this is not normal. I wouldn't diagnose it as "Anxiety Disorder" because there are other names, including OCD, and probably many more. I agree that you shouldn't use Wikipedia! It's not always a reliable source, since anyone can post information!
I think it's very wise for you to make a list of her behaviors. The more info you can give to a professional, the better. I agree with you that you need to try to shield your second child from these stresses, and get your 7 year old into a good program with a physician and a psychologist or other behaviorists/professionals who specialize in these issues. I have a cousin who has these issues and it's very frustrating for him but also has an impact on others in the family.
If the pediatric psychiatrist won't take your daughter's case, find someone who will. Unless you are happy with the psychologist with whom you have an appointment in 4 weeks. That person can probably refer you, as needed, for medical evaluations so you don't have to have all your eggs in the one psychiatrist's basket.
The bottom line is, you are not happy, your younger child is not happy, and your 7 year old is not happy. So you have to do something. You are doing the right thing by pursuing a variety of professional interventions.