If you babysit in your home, income you receive is taxable to you. It doesn't matter where the parents got the money.
If you babysit in their home, you are probably their household employee, and you must pay taxes on your income, and they must give you a W-2 and pay household employee tax. It doesn't matter where they got the money.
If you are a family member of the parents and the new foster child, then anything they pay you is probably not taxable, although that might get tricky if they need to show they are paying someone to qualify for reimbursement.
