Your non-military spouse needs to file form HW-4 with her civilian employer, so that HI state taxes are not withheld from her pay and she is not subject to paying taxes to the state of HI.
The form and instructions are at http://www.fmo.hawaii.edu/payroll/docs/Hawaii_State_Tax_Form_HW-4.pdf
Just curious, but during your in-processing briefing you received upon your arrival, were you not briefed on this? I certainly was when I first arrived in HI back in the 90's.
