Can my husband claim desertion because we are living apart?

Me and my husband of 14 years (we also have 2 minor kids) we spent a year in Italy. Then he returned to work in the US while I stayed back in Italy. We had agreed that I would stay in Italy one more year to give the kids continuity in school. But after 2 months he says he has found another woman and he mentioned divorcing me. I said I will not accept to divorce him. But a friend told me he can claim that I abandoned him because I remained in Italy when he went to the US. He moved to NY so I suppose the divorce would be in NY. Now I am scared and I don't know if I should reenter the US immediately with the kids. Even if I do that, he may refuse to come to live with us, and right now he lives in an apartment he shares with another person. What should I do?