I filed jointly with my wife on 5/14/2019. she originally filed for an extension because she is in the military prior to April 15, 2019. We were originally going to file married but separate because we weren't ready to file taxes before April 15th, as a result, she got the extension and I didn't file on the due date. On May 14, 2019 we decided to file jointly under her tax return and submitted it that day. We are due a federal refund but owe state taxes which we paid on May 14, 2019. Will we still receive a penalty for filing late even if we did it under her tax return and she filed an extension? If so, how much if we owed $544 for state taxes? Am i going to be charged the failure to pay penalty plus the failure to file penalty? Since we paid the $544 on May 14, 2019, how do we know how much the penalty/penalties will be? Are the penalties supposed to be paid the day you pay what you owe or is it mailed to you? Does what you owe accrue interest even if you don't know how much it is?
There will not be "any" late filing penalty from the IRS, becuase you did not owe the IRS any money - they owed you a refund.
For the state, you will owe at least interest on your late payment of state taxes. Remember, when you file an extention that only extends your time to file the return. It does not extend your time to pay taxes, if taxes are in fact, due. Now having paid the state taxes stopped the accumulation of interest on the amount you owed and paid. You can expect the state to bill you separately for any accumulated interest if owed. If your state also assessed a late filing penalty, then I would not know how that would be handled. I don't know what state the AD/MIL person is stationed in or what their "tax home" state is, and I also don't know the SLR of the non-military spouse.