We, yes and no. Let's say she was paid $100 per week. As an independent contractor she needs to estimate her taxes that will be owed, both federal and state income and self-employment, set some aside each week, and make quarterly payments to the IRS. The whole $100 was never hers to spend. As an employee at (for instance) Walmart, Walmart would withhold 7.65% social security and medicare tax and also a few dollars for state and federal income tax. Her take home might have been $80 a week. And Walmart is matching the social security so she really costs the company $108 per week even though she grosses $100.
If she had been treated as a household employee by the family at $100 per week, they would be required to send the IRS social security tax ($15 per week). They might have offered her $100 per week and paid the full $15 themselves, or they might have offered $100, withheld $7.65 and paid the other $7.65 themselves, or they might have just offered $85 per week. Household employers don't have to withhold income tax so that still would have been your daughter's responsibility to set aside and save up or make estimated payments.
When you start on a job like this you need to make taxes a part of the negotiations with the employer -- will you be an employee or contractor, and who covers the taxes. There's no way to know what might have happened if she had been treated as an employee instead. I think your daughter wasn't setting aside money and got surprised at the end, it's a tough but valuable lesson.
Generally speaking, if the care is in their home on their schedule she is an employee, if care is in her home she is a contractor, but it depends on the situation. The rules are discussed here. https://www.irs.gov/businesses/small-businesses-self-employed/independent-contractor-self-employed-o...
If she wants to file a complaint with the IRS asserting she should have been an employee, she can file an SS-8 form. If she is determined to have been an employee, she will get half her self-employment tax back. (The other half plus the income tax was always owed and it may have been her mistake to not plan ahead.) Filing the form will likely wreck any future chances of working for that family, though.
For the future, make sure she discusses the employee/independent issue with future potential clients before accepting the job, and consider the cost of taxes when setting her rate, and that she sets aside the right amount of estimated taxes.
Self employed or employee, you never get to spend your whole gross. There are always taxes, the only issue is who manages their collection, the employer or the self-employed person on their own.
