Generally speaking, if you and your wife are green card holders, you are required to file a US tax return to report all your worldwide income and pay income tax on it, no matter where you lived or where you earned the money. If you also pay foreign income taxes, you are allowed to claim either a deduction or a tax credit on your US tax return for foreign taxes that you pay.
I don’t know anything about Canadian tax law and can’t tell you how you would file in Canada, and whether you would be considered a resident or a non-resident. You would prepare your Canadian tax return first and pay the tax, in order to know what credit or deduction to apply on your US federal income tax return.
You didn’t mention this, but it is likely that you will be required to file a joint state tax return with your spouse as well. Even if you are living out of the country for the majority of the year, you will still be considered a resident of your state unless you have completely surrendered your state domicile. Your domicile is essentially your permanent tax home. If your job in Canada is in any way temporary and your spouse still lives in your state and you maintain a home with your spouse in your state, then you haven’t given up your state domicile, no matter how long you are away from the state.
If you are an independent contractor and file a schedule C, that would include self-employment tax, which gives you credits in the Social Security system. However, if you are an employee and you don’t file a schedule C, you will not get credits in the US Social Security system, and there is no legal way to report your income in such a way as to pay the extra tax and get those credits.
The US version of TurboTax can handle a situation where you work partly out of the country. There is a Canadian version of TurboTax but it is a different website and I have never used it.
