If your sister watches young children dependents, do you have to 1099? What about mom or dad?

There is no requirement for you to use a Form 1099-NEC when you pay someone to watch your children so that you can work.

If you are going to report the child care payments on your tax return for the Child and Dependent Care credit you will need the Social Security number of person who provided the child care.

Where is the babysitting taking place----in your own home or in your sister's home?  If it is in your own home, your sister might be a household employee, depending on how much she is being paid.  If she is a household employee, then you will need to issue a W-2 to her.

https://ttlc.intuit.com/turbotax-support/en-us/help-article/taxation/considered-household-employee/L8WWhbPfO_US_en_US?uid=lrtjhxqc

https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-payments/pay-taxes-pay-household-employee/L9eZxdOGo_US_en_US?uid=lrtjjefi

  If it is in her home, then she has self-employment income.   You do not issue a 1099NEC to her.  It is simply up to her to report that income on her own tax return; you need her SSN or Tax ID in order to enter the childcare credit on your own return.   The amount of income she enters on her tax return needs to match the amount you enter on your return for the credit.

And....you asked --"What about mom or dad?"    Again---where is the babysitting taking place----your own home or in the grandparent's home?