I cannot give tax advise but for information on the process for U.S. entry, contact your nearest U.S. Embassy or Consulate. If you need to contact an experienced immigration lawyer, click the Lawyer Search tab at the top of your screen to get to one using Avvo. Good luck and the best to you and family.
Options: I-131 Right Reenter Permit, Overseas DS-117 Returning Resident VIsa, or Relinguish LPR status:
Abandonment is the main issue on significant absences not based from employment, military, etc.
You may want to relinquish your Lawful Permanent Residency. If you do so, you can also file a tax form to the IRS, and a form to the USCIS/INS Abandonment of lawful permanent resident status is irrevocable. An individual who relinquishes lawful permanent resident status but wishes to regain it must qualify again for such status. Therefore, one should give careful thought before abandoning lawful permanent resident status.
If you wish to abandon your permanent resident status and relinquish your permanent resident card (also known as a green card and alien registration card), please appear at the USCIS overseas office to complete processing of Form I-407, Abandonment of Lawful Permanent Resident Status.
Print the Form I-407, complete it and bring it to USCIS overseas. If you are not able to access the form, you may receive one at the USCIS overseas Embassy public window. You must also bring a valid passport.
A copy of the signed and dated form will be given to you for your records. This copy of the completed I-407 is your receipt and it verifies that you have returned your permanent resident card to the U.S. Government or that your permanent resident card was previously lost or stolen. You should keep a copy of the completed I-407 in your passport whenever you travel to the United States.
Once the I-407 is completed, you will revert to your previous status as a non-resident of the United States. In order to visit the United States, you will need to comply with visa requirements for nationals of your country of citizenship. A nonimmigrant visas would be required for a temporary trip to the United States.
Relinquishing your permanent resident card and status does not affect your ability to apply to immigrate to the United States again in the future; however, you will have to apply through the usual application process from the beginning. SURRENDER THE LPR card if you are going to with the proper form at the US Consulate.
You are required to pay U.S. taxes otherwise-- you may be required to anyway, with the U.S. Citizen spouse. The IRS has a form also if you aren't a LPR anymore. You file both w/ the IRS/INS. You'll need to consult a tax atty. on that one esp. with the US Citizen issues. Other options are to reenter with a reentry permit, but if you truly are away for a decade or more-- could be pretty tough if only back in the U.S. for a few weeks to prove you haven't abandoned the LPR status which requires ties and intent to remain, pay taxes, often property, relatives, etc. I-131 for travel docs. and Returning Resident Visa DS-117 for those options.