The headcount is important because ADA only applies to companies with 15 or more; otherwise we'd have to see if IL has similar protections (e.g. in NY, companies with under 15 employees are covered by the NYS Human Rights Law, whose disability provisions mimic those of the ADA).
Technically, under ADA, they cannot arbitrarily require her to get a doctor's note stating fitness for duty and keep her from working until it's provided. By doing so, they're making potentially discriminatory assumptions about her condition and ability to work (i.e. they're "regarding her" as being disabled). Now, I doubt they're motives are nefarious, but small employers just don't have the resources or understanding of the law to really know what to do.
The proper procedure should be that her employer has a discussion with her first. This is referred to as the start of the "Interactive Process" under ADA in order to determine if a Reasonable Accommodation is necessary. They should provide her with a copy of her Job Description, and a medical certification request to give to her doctor. This form is similar to the FMLA Medical Certification, except that it is crafted to target the specific situation being evaluated. Unless she has a Description, how can the doctor assess fitness for duty?
Also, because this form contains Protected Health Information under HIPAA, the employer is restricted in who can view this information, and should have a policy designating who is entitled to view medical information. If they don't I'd look into a HIPAA release form.
The doctor would review the Description and questions, and determine if your daughter is capable of performing the "essential duties & responsibilities" of her position (few small businesses do this right). He would note any accommodations necessary and return the form to your daughter. She would return it to her employer ad they would have to determine if the accommodations amount to an Undue Hardship. In the case of your daughter, the need to have a fellow employee observe her for detrimental effects, or occasionally needing time away from work can hardly constitute Undue Hardship and would have to accommodate her. Current case law is allowing for Leaves of Absence for up to a year under ADA, so this certainly is less of a hardship than that.
Granted, this is a process that rarely happens quickly. It typically takes about 2 weeks to follow all the steps properly. If they insist that she cannot work without a release, I'd simply mention the potential ADA violations to them in an attempt to let them know you're no pushover, and hopefully they'd relent.
Obviously, you have to balance the effects this has on the work environment. By law, employees who seek assistance under ADA or any of the other laws under Title VII of the Civil Rights Act are protected from any retaliatory action. I wouldn't worry so much about co-workers as much as the higher-ups.
ADA isn't an easy law to understand or comply with. I've been doing compliance guidance for small businesses for 12 years, and I'm still learning new nuances every day. If anything isn't clear let me know and I'll try to clarify when I get a chance.
You can also use this link to the EEOC page on disability discrimination for guidance as well. http://eeoc.gov/laws/types/disability.cfm
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