You've asked no question so all I can say is that's the way those things work. If you are a W-2 employee the employer typically withholds income taxes with each paycheck as well as half the associated Social Security and Medicare. If you're an independent contractor then you typically need to make estimated tax payments quarterly and you are responsible for all the Social Security and Medicare taxes. That's why independent contractors usually demand a higher wage.
I assume your daughter was being paid on some sort of schedule - weekly, bi-weekly, etc. She didn't notice that she wasn't getting a payroll stub and that no taxes were being withheld? The good news here is that your daughter now knows in a tangible way the difference between being a bona fide "employee" vs. being an bona fide "independent contractor." That said, depending on the relationship between your daughter and the family she was baby sitting for, she very well might actually be an "employee" in the eyes of the IRS, and there are ways to press your case here.
