Yes. If you have a business, you need to give her a W-2; not a 1099-Misc. Your children, under 18, are exempt from FICA. As a 1099 recipient, she would have to pay self employment tax.
Ref: https://www.irs.gov/businesses/small-businesses-self-employed/family-help
If you are paying her for household work (e.g. baby sitting). her income does not need to be reported and does not qualify for the day care credit.
