My wife had a green card, but we live in Thailand. She had to return to the USA each year, of course. On the 3rd year, the immigration officer told her, "You don't live in the USA, so you don't qualify for the card. I'll let you in this time, but it will be confiscated next year if you aren't really residing in America."
The 10 year tourist visa is much better for your situation. Good luck.