Jesus Christ will be present Body, Blood, Soul and Divinity on the altar of the Church that she'll be attending. It's not like she's going to a Pentecostalist service headed by Pope Francis(oops, I meant to say Benny Hinn). In the past, Catholics have worshiped at Orthodox Churches, and Orthodox clergy and priests collaborated together in parish missions in parts of Eastern Europe where the schism between the two Churches wasn't so clearly defined(and when I say the past, I don't mean 1973. I'm talking about the Counter Reformation period, when Catholics were not too keen about ecumenical dialogue).
I think it's permissible to show proper respect at an Orthodox service, but we shouldn't receive Communion from them unless it's an emergency. But I don't see a problem with going to their Divine Liturgy. Just my own opinion, which I'm sure is about to be eviscerated.