| Actually, the tax refund your daughter is getting on her federal tax return has nothing to do with the tax refund she is entitled to on the State tax returns. The Federal tax refund is higher primarily due to the fact that she has withheld more in federal income taxes than she has withheld on her state taxes. Additionally, your daughter receives more deductions on her Federal Form 1040 than she does on State income tax returns.
Also, you right to assume that your daughter will only pay taxes for both her Maryland State and New York State based on her income earned in those states. Furthermore, there is no double taxation of income or wages on either the New York State or Maryland State Income Tax Return!
The difference in refunds on both states is again primarily due to the amount of both NY and MD State Income Taxes withheld. So, I would not arrive at the conclusion that either you or your tax preparer has erroneously filed your daughters individual multi-state income tax return. | 
