I am considered cheap by most peoples standards and I would need 225 per week for 2 children. So if you were paying the standard rate for 2 full-time kids, you would be paying almost 4000 more per year or more. So I say, hand her 4000 more dollars in exchange for her social security number LOL! .... NOT really. You are right. You should get the deduction and change providers. After you deduct this on her taxes, she'll likely quit anyway because she's going to be needing a better job in order to make the tax payments with penalties and interest.
She should be claiming it. If she isn't, it's probably because she's not well educated on how many deductions she can take and or she simply is not earning enough money to put aside tax money and still make a living. On one hand, it's not fair that she should make under the table money. But on the other hand, I understand what it's like to be a low income provider and not have anything left over after bill.
I have my husband claim zero deductions at work so that they take out too much. Then, I'm open 24 hours per day, 7 days per week. This allows me to take bigger deductions for my business than if I was open only traditional hours. I work my arse off for my tax savings and I'm not doing anything illegal.
If it were me, I would not want to help someone else commit tax fraud. But at the same time, I don't know enough information. Are you paying her enough money? Maybe you could compromise this year and claim less and next year pay her a little more. How many other kids does she have? If she is alone and without a spouse, her taxes should be pretty low if she has a few kids of her own to deduct. But if she is like me, ouch.. My husbands income is pretty good. He pushes me up into a higher tax bracket, my kids are moving out and our mortgage is paying down. Our deductions are slipping away and yet my living expenses only seem to go up. My husband is only willing to do so much. At some point in the next few years, I have to figure out a way to pay quarterly taxes and my daycare parents are going to have to start paying me more than they do now.