You get extra money to pay for off base daycare?
If yes, is that included in your taxable income, subject to withholding, and included on your W-2?
If yes again, then you are paying tax on your wages, you just happen to have higher wages than some other personnel. You pay tax on your wages, and you can claim whatever you pay in day care costs as your day care expense.
If no, then you need to tell us more about the program. What do you get from the Army and how do you pay for day care. On base or off? Is there any day care assistance recorded in box 10 of your W-2?