I work full time. If my wife worked full time we would be eligible to use a dependent care FSA. If my wife went to school full time we would be eligible to use a dependent care FSA. But my wife works half-time (20 hrs / week) and goes to school half-time. The resulting day care expenses are about the same as if she went to school full time and didn’t work. Are there allowances in the U.S. tax code for this situation?
FSA is a convenience to allow you to pay day care expenses with pre-tax money.
It sounds like neither you nor your wife are eligible through an employer, so you can't use one.
If you do not use FSA, then at tax time you can deduct the cost of day care from your gross income. In the end the effect is the same. Just keep track of your expenses.
Child care expenses aren't exactly deductible without the FSA, but if you can't use the FSA and end up paying them with after tax dollars, you can use these expenses to qualify for the Child and Dependent Care Tax Credit, which, depending on your circumstances, could save you more money than the FSA would have saved you.