We opened up a dependent childcare FSA through my husband's work for the year 2016. They have taken out the full $5,000 before we learned (by our own misinformation) that if both spouses do not work you cannot take advantage of this money. We can get reimbursement for around $1,600 of this knowing we'll have to pay taxes on it. How is any of this fixable? Can it be done in TurboTax, or will we need to hire a CPA?
Yes, it is fixable in turbotax.
You should apply for the maximum reimbursement you can prove with receipts. Since you do not qualify to exclude the money from your income, any money you use to pay child care expenses will be added back to your taxable income. But fortunately there is no extra penalty. Any money that is abandoned in the account is forfeited and simply disappears, it's not taxed or penalized, but you don't get it back. So you might as well get as much reimbursement as you can.
Turbotax can handle this situation in the dependent care interview. Your W-2 will show the amount of the FSA account, you will be asked if you forfeited any amounts, and turbotax will compute the tax on the non-qualified expenses that you did reimburse from the account.