You have to enter the Social Security number or Tax ID of the childcare provider you used in order to get the childcare credit. So your sister is going to need to amend her tax return after it has been processed. Otherwise she will eventually hear from the IRS about the unreported income. The IRS matches up that information.
She was trying to but turbo tax said she has to wait for her return to get rejected first and then amended it , but will I still get my refund or mines will be delayed as well ?
Yes, but it will flag your sister's return to the IRS.
You can go ahead and claim the dependent care credit and advise your sister to file an amended return. She will have to wait until her original return is fully processed (she gets her refund) before amending.
In addition to income tax, she will have to pay social security and Medicare tax (in the form of "self employment tax" [SET]), unless the total amount you paid her was less than $2230. SET is about 14%. But the income is earned income and may qualify her for more earned income credit.
Your refund will not be delayed. The IRS matching comes later.