The best way to address this is to start slowly and move forward with deliberate steps.
NY requires all earnings be reported on their W2; the detailed math will work it self out.
The tax codes are written in such a way you will not be double taxed.
When faced with multiple state returns to file, always prepare your home state LAST, That is so you can claim any and all taxes paid to other jurisdictions on your home state.
Prepare the NY return first, then Ohio, and finally Michigan.
The tax returns will seek actual wages earned in the state as well as the W2 reported income to determine tax liability.
