You are incorrect on the law. Tip credit is NOT supposed to be calculated hourly. Frankly, that would be next to impossible to do anyway because of the nature of table turnover. In a server's first hour of work, they may have 5 tables, but it's highly likely those tables won't pay their bill and thus leave a tip until the server's second hour of work. That doesn't mean the employer must pay full minimum wage during that hour.
The tip credit is calculated per payweek. Most, if not all, restaurants will have servers claim their tips daily as it is easiest to do. At the end of the week, the total tips are calculated by the employer based on what the employee reported and added to the hourly rate. That is then divided by the number of hours in the payweek that the employer worked. As long as the average hourly TOTAL pay for the entire payweek is equal to or greater than minimum wage, then the employer does not need to do anything. The employer would only be responsible for increasing the employee's pay if their tips+ hourly wage averaged for the entire week was less than minimum wage.
Assuming your DD works 4-5 hour shifts (standard in restaurants for minors), and she's making $30-$40 in tips per shift, plus the ~$14-18 hourly pay that shift, it sounds like she's averaging more than minimum wage.
And the taxes she pays are be based on everything she makes- hourly wage plus tips. Servers are required to report all tips (including cash tips) and pay taxes on all tips, even when it exceeds minimum wage (which is essentially always the case).