Yes, it could qualify for the dependent care credit. If your sister does not operate a child daycare facility you will have to use your sister's social security number when you file your tax return and claim the dependent care credit. Your sister would have to report this income on her tax return. If she does not report the income the IRS will contact her at some point in the near future asking why she did not report the income from providing child care services.
Thanks for the help! I got one more question to ask.
Won't the fact that we live in 2 different states throw up a red flag in the IRS computer algorithm?